Kinematics 1r

Master Your Physics - NEET / AIIMS

KINEMATICS -1

PMT SYLLABUS Frame of reference. reference. Motion Mot ion in a straight line: Position -time graph, speed and velocity. velocity. Uniform and non-unifor motion, average speed and instantaneous velocity. Uniformly accelerated motion, velocity-time, position-time graphs, relations for uniformly accelerated motion (graphical treatment). Elementary concepts of differentiation diff erentiation and integrat ion for describing describi ng motion.

1.

Th Theory

3-46

2.

Exercise 1 (Theoretical Questions)

47-51

3.

Exercise 2 (Objective Questions)

52-63

5.

Exercise 3 (Previsouly Asked)

64-69

4.

Exercise 4 (Assertion & Reason)

70-72

4.

Answers

73-75

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Tarun Mankad (M.Tech. - IIT Kanpur)


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KINEMATICS -1



1.

KINEMATICS -1

INTRODUCTION The branch of physics which deals with the study of motion of material objects i s called mechanics. Mechanics is divided into following branches. (i) Statics :

Statics is the branch of mechanics mechanics which deals with the study of motion of objects under the effect of forces in equilibrium. (ii) Kinematics :

It is that branch of mechanics which deals with the study of motion of object without taking into account the factors (i.e. nature of forces, nature of bodies etc.) which cause motion. Here time factor plays an essential role. (iii) Dynamics :

It is that branch of mechanics which deals with the study of motion of objects taking int o account the factors which cause motion. Presently we shall study kinematics. Rest : An object is said to be at rest if it does not change its position with time, with respect to its

surroudings. A book lying on a table, a person sitting si tting in a chair are the examples of rest. Motion : An object is said to be in motion if it changes its position with time, with respect

to its surroundings. Example : A bird flying in air, a train moving on rails, a ship sailing on water, a man walking on

road are some of the examples of motion, visible to the eye. Motion of gas molecules is an example of motion, invisible to the eye. Rest & Motion are relative terms :

When we say that an object is at rest or in motion,then this statement is incomplete and meaningless. Basically, Basically, rest & motion are relative terms. An object which is at rest can also be in motion simultaneously. taneously. This can be illustrated as follows. The passengers sitting in a moving bus are at rest with respect to each other but they are also in motion at the same same time with respect to the objects objects like trees, buildings on the road side. So the motion and rest are relative terms. Rectilinear motion :

If a particle moves in a fixed direction, the motion of this type is called rectilinear motion or one dimensional motion. For example the motion of an ant on a wire is a rectilinear motion. Two dimensional mo tion :

If the motion of a particle is i s in such a way that i ts position remains on a fixed fi xed plane, then the motion of a particle is called two dimensional motion. For example the motion of a rolli ng ball on a horizontal plane or earth’s surface, is a two

dimensional motion. Three dimensional motion :

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KINEMATICS -1

If a line or plane is not fixed for the motion of a particle, then its motion is called thr ee dimensional motion. For example the motion of a flying bird is a three dimensional motion. 2.

DISTANCE

The length of the actual path between initial & final positions of a particle in a given interval of time is called distance covered by the particle. Distance is the actual length of the path. It is the characteristic property of any path ie., path is always associated when we consider distance between two positions. Distance beteen A & B while moving through path (1) may or may not be equal to the distance between A & B while moving through path (2) II

Characteristics of Distance :

(i) It is a scalar quantity.

A

(ii) It depends on the path.

B

I

(iii) It never reduces with time. (iv) Distance covered by a particle is always positive & can never be negative or zero. (v) Dimension :

M

0

1

L T



0

(vi) Unit : In C.G.S.system centimeter (cm), In S.I. system metre (m). 3.

DISPLACEMENT

The shortest distance from the initial position to the final position of the particle is called displacement. The displacement of a particle is measured as the change in the position of the particle in a particular direction over a given time interval. It depends only on final & initial positions. Displacement of a particle is a position vector of its final position w.r.t. initial position. 

Position vector of A w.r.t. O  OA





r A



A

Y

x1 î  y1 jˆ  z1 kˆ

B 

Position vector of B w.r.t. O  OB





rB

O

 x2 î  y2 ˆj  z2kˆ

Displacement





AB   x 2

 x1  î   y 2  y1  ˆj   z2  z1  kˆ

X

Z

Characteristics of Displacement :

(i) It is a vector quantity. (ii) The displacement of a particle between any two points is equal to the shortest distance between them. (iii) The displacement of an object in a given time interval can be positive, negative or zero. 0 1 0 (iv) Dimension : M L T 

(v) Unit : In C.G.S. centimeter (cm), In S.I. system meter (m).

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KINEMATICS -1

COMPARATIVE STUDY OF DISPLACEMENT AND DISTANCE S.No. Displacement

Distance

1.

It has single value bewteen two points

It may have more than one value between two points

2.

0  Displacement  0

Distance > 0

3.

Displacement can decrease with time

It can never decrease with time.

4.

It is a vector quantity

It is a scalar quantity

Special note:

1. The actual distance travelled by a particle i n the given interval of time is always equal to or greater than the magnitude of the displacement and in no case, it is less than the magnitude of the displacement, i.e., Distance  | Displacement | 2. Displacement may be + ve, – ve or zero. 3. Distance, speed and time can never be negative. 4. At the same time particle cannot have two positions. Some Impossible graphs :

e+ c nO a t s i – D

time

t n e m e c a l p s i D O

d e e p s

time

t1 time

Example 1.

An old person moves on a semi circular track of radius 40 m during a morning walk. If he starts at one end of the track and reaches at the other end. Find the displacement of the person. Sol. Displacement = 2R = 2 x 40 = 80 meter. Example 2.

An athelete is running on a circular track of radius 50 meter. Calculate the displacement of the athlete after completing 5 rounds of the track. Sol. Since final and initial positions are same .

Hence displacement of athlete will be

r  r  r  0

Example 3.

If a particle moves from point A to B then distance covered by particle will be. Sol. D = x + 2x = 3x Example 4.

A monkey is moving on circular path of radius 80 m. Calcualte the distance covered by the

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KINEMATICS -1

monkey. Sol. Distance = Circumference of the circle D  2R

 D  2  80  160  3.14  502.40m

Example 5.

A man has to go 50 m due north, 40 m due east and 20 m due south to reach a field. (a) What distance he has to walk to reach the field? (b) What is his displacement from his house to the field?

N

Sol. Let origin be O then W

(a) Distance covered

= OA + AB + BC

E

= 50 + 40 + 20 S

= 110 meter (b) First method :

Second method : 

Displacement OC = =

OD2 40

2

= 10 25

Displacement d  50ˆj  40iˆ  20 ˆj

 CO2

 30

= 30 ˆj  40 î

2

40m

B 20m

50m



 50 meter

A

C

| d |  40 2  30 2 = 50 meter



D

O

Example 6.

A body covers

1 th part of a circular path. Calulate the ratio of distance and displacement. 4

Sol. Distance = AB from path (1)

=

2r 4



Displacement = AB

r

=

2 =



OA 2

r

2

B 1

 OB2

r r 2 2

O

r

A

r / 2  Distance   Displacement r 2 2 2

Example 7.

A point P consider at contact point of a wheel on ground which rolls on ground without sliping then value of displacement of point P when wheel completes half of rotation - [If radius of wheel is 1 m] Sol. Displacement =

2  4

Ans. P 2r P

r

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KINEMATICS -1

Practice Problem - 1 (A) 10 2m 1. 2.

Can displacement be greater than distance travelled by an object ? Under what condition will the distance and dis placement of a moving object will have the same magnitude ?

(C) 7.

10 2

(B) 10m

m

(D) 10  2m

A man goes 10m towards North, then 20m towards east then displacement is

3.

Can a body have a velocity and speed equal ?

(A) 22.5m

(B) 25m

4.

Is magnitude of the displacement of an object and total distance covered by it in certain time interval same ? Explain.

(C) 25.5m

(D) 30m

5.

A person moves 30 m north and then 20 m towards east and finally 30 2 m in southwest direction. The displacement of the person from the origin will be

Here are three pairs of initial and final positions, respectively, along an x axis. Which pairs give a negative displacement : (A) –3 m, +5 m; (B) –3 m, –7 m; (C) 7m, –3 m ?

6.

8.

(A) 10 m along north (C) 10 m along west 9.

A Body moves 6 m north. 8 m east and 10m vertically upwards, what is its resultant displacement from initial position

(B) 10 m long south (D) Zero

An aeroplane flies 400 m north and 300 m south and then flies 1200 m upwards then net displacement is (A) 1200 m

(B) 1300 m

(C) 1400 m

(D) 1500 m *****

5.

SPEED

Speed of an object is defined as the time rate of change of position of the object in any direction. It is measured by the distance travelled by the object in unit time in any direction. i.e.,

speed=

distance travelled time taken

(i) It is a scalar quantity. (ii) It gives no idea about the direction of motion of the object. (iii) It can be zero or positive but never negative. (iv) Unit: C.G.S. cm/sec, S.I. m/sec,

1km / h =

100 5  m/s 60  60 18

1 km / h 

5 m/s 18

(v) Dimension : M0 L1 T 1 Types of speed :

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KINEMATICS -1

Uniform speed : An object is said to be moving with a uniform speed, if it covers equal distances

in equal intervals of time, how soever small these intervals may be. The uiform speed is shown by straight line in distance time graph. For example: suppose a train travels 1000 metre in 60 second. The train is said to be moving with

uniform speed, if it travels 500 metre in 30 second, 250 metre in 15 second, 125 metre in 7.5 second and so on. (b)

Non Uniform Speed : An object is said to be moving with a variable speed if it covers equal distance

in unequal intervals of time or unequal distances in equal intervals of time, howsoever small these intervals may be. For example : suppose a train travels first 1000 metre in 60 second, next 1000 metre in 120 second

and next 1000 metre in 50 second, then the train is moving with variable speed. (c)

Average Speed : When an object is moving with a variable speed, then the average speed of the

object is that constant speed with which the object covers the same distance in a given time as it does while moving with variable speed during the given time. Average speed for the given motion is defined as the ratio of the total distance travelled by the object to the total time take i.e.,

Average speed V =

total distance travelled total time taken

Note : If any car covers distance x1, x2, ........... in the time intervals t1, t2, ....... then.

V=

x1  x 2

 x3  .......  xn t1  t 2  .....  tn

SOME IMPORTANT CASES RELATED TO AVERAGE SPEED : Case : 1

If body covers distances x1, x2, and x3 with speeds v1, v2, and v3 respectively in same direction then average speed of body.



V

V





x1  x 2

 x3 t1  t 2  t 3

x1  x 2 x1 x 2  v1 v 2

here, t1



x1 , t2 v1

 x3 



x2 v2

V1

x3 v3

, t3



x3 v3

V2

V3 x

x' O

x1

x2

If body covers equal distances with different speeds then, x1

V



x1 v1



3x x x  v2 v3



1 v1



3 1 v2



1 v3



x3

 x2  x 3  x

3v1v2 v 3 v1v 2

 v 2 v 3  v 3 v1

Case : 2

If any body travels with speeds v1,v2,v3 during time intervals t1,t2,t3 respectively then the average speed of the body wil be Average speed V

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

x1  x 2

 x3 v1t1  v2 t2  v3 t3  t1  t 2  t 3 t1  t2  t3

If t1

 t2  t 3  t


Master Your Physics - NEET / AIIMS  (d)

 v1  v 2  v 3   t 3t



KINEMATICS -1

 v1  v 2  v 3  3

Instantaneous speed :

The speed of the body at any instant of ti me or at a particular position is called instantaneous speed. Let a body travel a distance When

 x in the time interval  t , then its average speed 

x . t

t  0 , then average speed of the body becomes the instantaneous speed.

Instantaneous speed =Lim t 0 

x dx  t dt

(to be studied later)

Note :

(a) Speedometer of the vehicle measures its instantaneous speed. (b) In case of a uniform motion of an object, the instantaneous speed is equal to its uniform speed. 6.

VELOCITY

It is defined as rate of change of displacement. Characteristics of Velocity :

(i) It is a vector quantity.

(ii) Its direction is same as that of displacement.

(iii) Unit and dimension : Same as that of speed. Types of Velcoity :

(a) Instantaneous Velocity

(b) Average Velocity

(c) Uniform Velocity (a)

(d) Non-uniform Velocity

Instantaneous Velocity : It is defined as the velocity at some particular instant.

 r dr  (to be studied later) Instantaneous velocity  lim t 0 t dt 



Total Displacement Total time

(b)

Average Velocity : Average Velocity =

(c)

Uniform Velocity : A particle is said to have uniform velocity, if magnitudes as well as direction of its velocity remains same and this is possible only when the particles moves in same straight line

reservering its direction. (d)

Non-uniform Velocity : A particle is said to have non-uniform velocity, if either of magnitude or direction of velocity changes (or both changes).

7.

COMPARATIVE STUDY OF SPEED AND VELOCITY

S.No.

1. 2.

Speed

Velocity

It is the time rate of change of distance of a body. of a particle It tells nothing about the direction of motion

It is the time rate of charge of displacement It tells the direction of motion of the particle

of the particle 3.

It can be positive or zero

It can be positive or negative or zero

4.

It is a scalar quantity

It is a vector quantity

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KINEMATICS -1

Example 8.

A car travels a distance A to B at a speed of 40 km/h and returns to A at a speed of 30 km/h. (i) What is the average speed for the whole journey? (ii) What is the average velocity ? Sol. (i) Let AB = s, time taken to go from A to B, t1 =

and time taken to go from B to A,

 total time taken = t1 + t2 =

t2 =

s h 40

s h 30

 3  4  s 7s s s h    40 30 120 120

Total distance travelled = s + s = 2s

 Average speed 

total distance travelled 2s  total time taken 7s / 120



120  2 7

 34.3 km/ h

(ii) Total displacement = zero, since the car returns to the original position. Therefore, average velocity 

total displacement 0  0 time taken 2t

Example 9.

From the adjoining position time graph for two particles A and B the ratio of velocities vA : v B will be [1] 1 : 2

Sol.

V A VB



tan a tan b

[2] 1: 3



tan 300 tan60

0



[3]

1/ 3 3



1

[4] 1 : 3

3 :1

Ans. [4]

3

Example 10.

In a car race, car A takes a time of t sec. less than car B at the finish and passes the finishing point with a velocity  m/s more than the car B. Assuming that the cars start from rest and travel with constant accelerations a1 and a2 respectively, show that v =

 a1a2  t  

Sol. Let the time taken by two cars to complete the journey be t 1 and t2 and their velocities at the finish

be

1 and 2 respectively..

Given that, t1

 t 2  t and 1  2  

Now S1  S 

1 2

a1t12 and S 2  S 

(At start, v1 = v2 = 0)

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1 2

a 2t 22

............ (1)

............ (2) ............ (3)


Master Your Physics - NEET / AIIMS a1t12

Hence

KINEMATICS -1

 a2 t 22  2s

B

Also,

v 1  a1t1 and v 2

or

v1t1 = a1t12 = 2s and v2t2 = a2t22 = 2s 2s t2 v 1 and



t1



So,

t2

 t1  2s 



t n e m e c a l p s i D

 a2t 2

O

A 60º 30º Time

2s v2

 1 1   v  2 v1 

............ (4)

From equations (1) and (4) we have

2s

 1 1 v  v   t 1  2  v1  v 2   v   t or 2s   t  v1v 2   v 1v 2 

or 2s 

 v 2 v 2  v v  or v   1 2  t   1 22   t  ( 2s)   2s 

 v1v 2    × t = (a a )  t 1 2 t t  1 2 

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KINEMATICS -1

Practice Problem - 2 8. 1.

Can an object have constant speed but variable velocity ?

2.

Can the speed of a body be negative ?

3.

Can a body have a velocity and speed equal ?

4.

Show that average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.

5.

6.

An athlete completes one round of a circular track of radius R in 40 seconds. What will be the displacement at the end of 2 min. 20 second ? You drive a beat-up pickup truck along a straight road for 8.4 km at 70 km/h, at which poin the truck runs out of gasoline and stops. Over the next 30 min, you walk another 2.0 km farther along the road to a gasoline station.

An automobile travels on a straight road for 40 km at 30 km/h. It then continues in the same direction for another 40km at 60 km/h. (A) What is the average velocity of the car during this 80 km trip ? (Assume that it moves in the positive x direction.) (B) What is the average speed ?

9.

Compute your average velocity in the following two cases : (A) You walk 73.2 m at a speed of 1.22 m/s and then run 73.2 m at a speed of 3.05 m/s along a straight track. (B) You walk for 1.00 min at a speed of 1.22 m/s and then run for 1.00 min at 3.05 m/s along a straight track.

Objective Questions 10. A car travels from A to B at a speed of 20 km / hr and returns at a speed of 30 km / hr .

(A) What is your overall displacement from the beginning of your drive to your arrival at the station ?

The average speed of the car for the whole journey is (A) 25 km / hr

(B) 24 km / hr

(B) What is the time interval t from the beginning of your drive to your arrival at the station ?

(C) 50 km / hr

(D) 5 km / hr

(C) What is your average velocity

avg from the

beginning of your drive to your arrival at the station? Find it both numerically and graphically. 7.

Figure shows four paths along which objects move from a starting point to a final point, all in the same time. The paths pass over a grid of equally spaced straight lines. Rank the paths according to (A) the average velocity of the objects and (B) the average speed of the objects, greatest first.

11. A boy walks to his school at a distance of 6 km with constant speed of 2.5 km/hour and walks back with a constant speed of 4 km/hr . His average speed for round trip expressed in km/hour , is

(A) 24/13

(B) 40/13

(C) 3

(D) 1/2

12. A car travels the first half of a distance between two places at a speed of 30 km/hr and the second half of the distance at 50 km/hr . The average speed of the car for the whole journey is

(A) 42.5 km/hr

(B) 40.0 km/hr

(C) 37.5 km/hr

(D) 35.0 km/hr

13. One car moving on a straight road covers one third of the distance with 20 km/hr and the rest with 60 km/hr. The average speed is

(A) 40 km/hr (C) 46

Page # 12

2 km/hr 3

(B) 80 km/hr (D) 36 km/hr


Master Your Physics - NEET / AIIMS 14. A car moves for half of its time at 80 km/h and for rest half of time at 40 km/h. Total distance covered is 60 km. What is the average speed of the car

(A) 60 km / h

(B) 80

(C) 120

(D) 180

(A) 50

(B) 53.33

(C) 48

(D) 70

(B) 68 sec

(C) 80 sec

(D) 92 sec

1 2

v1v 2

v1  v 2 2

5v1v 2

2v1v 2

(C) v  v 1 2

(D) 3v  2v 1 2

(A) Less than one (B) Equal to one (C) Equal to or less than one

17. A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total distance covered by the particle during this time is 30m. Which of the following statements about the motion of the particle is false

(A) Displacement of the particle is zero (B) Average speed of the particle is 3 m/ s (C) Displacement of the particle is 30 m

(D) Equal to or greater than one 20. A particle moves for 20 seconds with velocity 3 m/s and then velocity 4 m/s for another 20 seconds and finally moves with velocity 5 m/ s for next 20 seconds. What is the average velocity of the particle

(A) 3 m/s

(B) 4 m/s

(C) 5 m/s

(D) Zero *******

(D) Both (A) and (B)

8.

(B)

19. The numerical ratio of displacement to the distance covered is always

16. A 150 m long train is moving with a uniform velocity of 45 km/h. The time taken by the train to cross a bridge of length 850 meters is

(A) 56 sec

18. If a car covers 2/5 of the total distance with v1 speed and 3/5th distance with v2 then average speed is

(A)

15. A train has a speed of 60 km/h. for the first one hour and 40 km/h for the next half hour. Its average speed in km/h is

KINEMATICS -1 th

ACCELERATION

It is defined as the rate of change of velocity. (i) It is a vector quantity. (ii) Its direction is same as that of change in velocity and not of the velcoity (That is why, acceleration in circular motion is towards the centre). (iii) There are three ways possible in which change in velocity may occur.

When only direction

When only magnitude changes

To change the direction, net acceleration or net force should be perpendicular to direction of veloc ity.

In this case, net force or net acceleration should be parallel or antiparallel to the direction of velocity. (straight line motion)

Uniform Ex : motion.

Ex : When ball is thrown up under gravity.

Page # 13

circular

When both the direction changes and magnitude change In this case, net force or net acceleration has two components. One component is parallel or antiparallel to velocity and another one is perpendicu lar to velocity. Ex : Projectile motion



KINEMATICS -1

Types of acceleration (a) Instantaneous acceleration : It is defined as the acceleration of a body at some particular instant. 

Instantaneous acceleration = lim t 0



(b) Average acceleration = aav



v dv  dt t 





 v v 2  v1   t t 2  t1

(c) Uniform acceleration : A body is said to have uniform acceleration if magnitude and direction

of the acceleration remains constant during particle motion. Note : If a particle is moving with uniform acceleration, this does not necessarily imply that particle

is moving in straight line. Example : Parabolic motion


(d) Non-uniform acceleration : A body is said to have non-uniform acceleration, if magnitude or

direction or both, change during motion. Note : (i) Acceleration is a vector with dimensions [LT –2] and SI units (m/s2) (ii) If acceleration is zero, velocity will be constant and motion will be uniform. (iii) However if acceleration is constant acceleration is uniform but motion is non-uniform and if

acceleration is not constt. both motion and acceleration are non-uniform. 





(iv) If a force F acts on a particle of mass m then by Newton’s law a  F/ m 



(v) As by definition , v 

ds dt

so,



a





dv dt



d dt

     ds  d2 s  dt   2   dt  




i.e. if s is given as a function of time, second time derivative of displacement gives acceleration. (vi) If velocity is given as function of position then by the chain rule a 

[as

dx dt

dv dt



dv dx .  dx dt

a  v

dv dx

=v]



(vii) As acceleration a 



dv dt



, the slope of velocity time graph gives acceleration i.e. a 



dv dt

= tan

(viii) Acceleration can be positive or negative. Positive acceleration means velocity is increasing with

time while negative acceleration called retardation means velocity is decreasing with time.

Page # 14



KINEMATICS -1

Practice Problem - 3 1.

The direction in which an object moves is given by the direction of velocity of the object and not by the direction of acceleration. Explain this statement with suitable example.

11. The correct statement from the following is

(A) A body having zero velocity will not necessarily have zero acceleration

2.

Can a body have zero velocity and still be accelerating ?

(B) A body having zero velocity will necessarily have zero acceleration

3.

Can the direction of velocity of a body change, when acceleration is constant ?

(C) A body having uniform speed can have only uniform acceleration

4.

A car manufacturer advertises that the brakes are so perfect that the car stops instantaneously. Comment.

(D) A body having non-uniform velocity will have zero acceleration

5.

Which of the two; velocity or acceleration decides the direction of motion of a body ? Ex plain with the help of an example.

6.

Give examples to show that a positive acceleration can be associated with a ‘slowing down’ and a negative acceleration with a ‘speeding up’.

7.

Can an object be accelerated without speeding up or slowing down ?

8.

A wombat moves along an x axis. What is the sign of its acceleration if it is moving (a) in the positive direction with increasing speed, (b) in the positive direction with decreasing speed, (c) in the negative direction with increasing speed, and (d) in the negative direction with decreasing speed.

12. For a moving body at any instant of time

(A) If the body is not moving, the acceleration is necessarily zero (B) If the body is slowing, the retardation is negative (C) If the body is slowing, the distance is negative (D) If displacement, velocity and acceleration at that instant are known, we can find the displacement at any given time in future 13. Acceleration of a particle changes when

9.

(A) Direction of velocity changes (B) Magnitude of velocity changes (C) Both of above (D) Speed changes ******

A particle had a speed of 18 m/s at a certain time, and 2.4 s later its speed was 30 m/s in the opposite direction. What were the magnitude and direction of the average acceleration of the particle during this 2.4 s interval ?

10. An automobile driver increases the speed at a

constant rate from 25 km/h to 55 km/h in 0.50 min. A bicycle rider speeds up at a constant rate from rest to 30 km/h in 0.50 min. Calculate their accelerations ?

Page # 15



KINEMATICS -1

Interpretation of Motion Using Graphs

During motion of the particle its parameters of kinematical analysis (v, a, s) changes with time. This can be represented on the graph. Position Time Graph Position time graph is plotted by taking time t along x-axis and position of the particle on y-axis.

Let AB is a position-time graph for any moving particle As Velocity =

Change in position y 2  y1  t 2  t 1 Time taken

BC From triangle ABC , tan  AC



AD AC

 y1  t 2  t 1 y2

y

…(i)

….(ii)

y t i c o l e V

v 2

D

v 1

B 

C

A

By comparing (i) and (ii) Velocity = tan v = tan

O

t 1

t 2

x

Time

It is clear that slope of tangent on po sition-time graph represents the velocity of the particle. P

1.

 = 0° so v = 0 i.e., line parallel to time axis represents that the particle is O

T

at rest. P

= 90° so v =  i.e., line perpendicular to time axis represents that particle is



 O

T

changing its position but time does not changes it means the particle possesses infinite velocity. Practically this is not possible. P

3.

= constant so v = constant, a = 0 i.e., line with constant slope represents uniform

 O

T

velocity of the particle. P



 O

is increasing so v is increasing, a is positive.i.e., line bending towards position

T

axis represents increasing velocity of particle. It means the particle possesses acceleration.

Page # 16



KINEMATICS -1

P

5.

is decreasing so v is decreasing, a is negative i.e., line bending towards time



O

T

axis represents decreasing velocity of the particl e. It means the particle possesses retardation. P





 O

constant but > 90o so v will be constant but negative i.e., line with negative

T

slope represent that particle returns towards the point of reference. (negative displacement).

P A

B C

7.

Straight line segments of different slopes represent that velocity of the body O

T S

changes after certain interval of time. P T

8.

O

This graph shows that at one instant the part icle has two positions, which is

not possible. P

9. O

T

The graph shows that particle coming towards origin initiall y and after that it is

moving away from origin. Note : If the graph is plotted between distance and time then it is always an increasing curve and it

never comes back towards origin because distance never decrease with time. Hence such type of distance time graph is valid up to point A only, after point A, it is not valid as shown in the figure.

e c n a t s i D

A

O

Time Fig. 2.9

Page # 17



KINEMATICS -1

Velocity-time Graph

The graph is plotted by taking time t along x-axis and velocity of the particle on y-axis. Calculation of Distance and displacement : The area covered between the velocity time graph and

time axis gives the displacement and distance travelled by t he body for a given time interval. Total distance | A1 || A2 || A3 | = Addition of modulus of different area. i.e. s  | |dt Total displacement  A1  A2  A3 = Addition of different area considering their sign. i.e. r    dt Area above time axis is taken as positive, while area below time axis is taken as negative + 1

3

t 2 – 

Table : Various velocity -time graphs and their interpretation



y t i c o l e V

= 0°, a = 0, v = constanti.e., line parallel to time axis represents that the particle is



O

moving with constant velocity.

2.

y t i c o l e V

= 90o, a = , v = increasing i.e., line perpendicular to time axis represents that the



O

Time

particle is increasing its velocity, but time does not change. It means the par ticle possesses infinite acceleration. Practically it is not possible.

3.

y t i c o l e V

O

= constant, so a = constant and v is increasing uniformly with time i.e., line with



Time

constant slope represents uniform acceleration of the parti cle.

Page # 18



4.

y t i c o l e V

KINEMATICS -1

increasing so acceleration increasing i.e., line bending towards velocity axis represent



O

Time

the increasing acceleration in the body.

5.

y t i c o l e V

decreasing so acceleration decreasing i.e. line bending towards time axis represents



O

Time

the decreasing acceleration in the body

6.

y t i c o l e V

Positive constant acceleration because  is constant and < 90o but initial velocity

O

Time

of the particle is negative.

7.

y t i c o l e V

Positive constant acceleration because  is constant and < 90o but initial velocity of

O

Time

particle is positive.

9.

y t i c o l e V

Negative constant acceleration because  is constant and > 90o but initial velocity of

O

Time

the particle is positive.

10.

y t i c o l e V

Negative constant acceleration because  is constant and > 90o but initial velocity

O

Time

of the particle is zero. y t i c o l e V

11.

O

Time

Negative constant acceleration because  is constant and > 90 o but initial velocity of

the particle is negative.

Page # 19



KINEMATICS -1

Example 11.

Describe the motion shown by the following velocity-time graphs.

(a)

(b)

Sol.(a) During interval AB: velocity is +ve so the particle is moving in +ve direction, but it i s slowing down

as acceleration (slope of v-t curve) is negative. During interval BC: particle remains at rest as velocity is zero. Acceleration is also zero. During interval CD: velocity is -ve so the particle is moving in -ve direction and is speeding up as acceleration is also negative. (b)

During interval AB: particle is moving in +ve direction with constant velocity and acceleration is zero. During interval BC: particle is moving in +ve direction as velocity is +ve, but it slows down until it

comes to rest as acceleration is negative. During interval CD: velocity is -ve so the particle is moving in -ve direction and is speeding up as acceleration is also negative.

Important Points to Remember



For uniformly accelerated motion (a  0), xt graph is a parabola (opening upwards if a > 0 and opening downwards if a < 0). The slope of tangent at any point of the parabo la gives the velocity at that instant.



For uniformly accelerated motion (a  0), vt graph is a straight line whose slope gives the acceleration of the particle.



In general, the slope of tangent in xt graph is velocity and the slope of tangent in vt graph is the acceleration.

 

The area under a t graph gives the change in velocity.



The area between the vt graph gives the distance travelled by the particle, if we take all areas as positive. Area under vt graph gives displacement, if areas below the taxis are taken negative.

Example 12.

For a particle moving along x-axis, velocity-time graph is as shown in figure. Find the distance travell ed and displacement of the particle? Sol. Distance travelled = Area under v-t graph (taking all areas as +ve.)



Distance travelled = Area of trapezium + Area of triangle =

1 2

1

2  6 8 +  4  5 2

= 32 + 10 = 42 m Displacement = Area under v-t graph (taking areas below time axis as -ive.)  Displacement = Area of trapezium  Area of triangle =

1 2

1

2  6 8   4  5 2

= 32  10 = 22 m Hence, distance travelled = 42 m and displacement = 22 m.

Page # 20



KINEMATICS -1

Practice Problem - 4 10. Find the angle between the x-axis and the line

1. Find the inclination of the line whose slope

is 

1 3

joining the points (,3 –1) and (4, –2). 11. Consider the following population and year

.

graph (Fig.), find the slope of the line AB and using it, find what will be the population in the

2. Find the slope of the line through the points

year 2010 ?

(4, –6), (–2, –5). 3. Determine  , so that 2 is the slope of the

line through (2, 5) and  ,3 . 4. Show that the line joining the points (2, –3)

and (–5, 1) is parallel to the line joining (7, –1) and (0, 3). 5. Find the equation of the straight line paral-

13. Passing through the point (–4, 3) with slope

lel to y-axis and at a distance (i) 3 units to the right

12. Write the equations for the x and y-axes.

(ii) 2 units to the

1 2

left. 6. Find the equation of the straight line paral-

14. Passing through (0, 0) with slope m. 15. Find angles between the lines

lel to x-axis and at a distance (i) 5 units above the x-axis

.

( ii )

9

3 x  y 1 and

x  3 y  1.

units below the x-axis. 7. Find the equation of the straight line which

passes through the point (2, –3) and is

16.The acceleration of a moving body can be found

from

(i) parallel to the x-axis (ii) perpendicular to the x-axis

(A) Area under velocity-time graph (B) Area under distance-time graph

8. Find the slope of the lines :

(C) Slope of the velocity-time graph

(a) Passing through the points (3, –2) and (–1, 4), (b) Passing through the points (3, –2) and (7, –2),

(D) Slope of distance-time graph 17. A man goes 10m towards North, then 20m

(c) Passing through the points (3, –2), and (3, 4),

towards east then displacement is

(d) Making inclination of 60o with the positive di-

(A) 22.5m

(B) 25m

(C) 25.5m

(D) 30m

rection of x-axis. 9. Find the slope of the line, which makes an angle

of 30o with the positive direction of y-axis measured anticlockwise.

Page # 21



KINEMATICS -1


2.

An object is in uniform motion along a straight line. What will be position-time graph for the motion of the object if (a) x0 = +ve, v = +ve (b) x0 = +ve, v = –ve (c) x 0= –ve, v = +ve and (d) both x0 and v are negative? The letters x0 and v represent position of the object at time t = 0 and uniform velocity of the object respectively. Is the time variation of position, shown in figure observed in nature?

11. How is the velocity-time graph of accelerated

motion helpful in studying the motion of the object in one dimension? 12. How is the position-time graph of uniformly

accelerated motion in one dimension helpful in studying the motion of the object? 13. What is the acceleration of a body when its

velocity-time graph is (i) perpendicular to time axis. (ii) parallel to time axis? 14. What do the slopes of ‘distance - time’ and

TIME

POSITION

3.

angles of 30° and 45° with the time axis. What is ratio of the velocities vA : vB ?

Two straight lines drawn on the same displacement-time graph make angles 30º and and 60° with time-axis respectively fig. Which line represents greater velocity? What is the ratio of two velocities?

‘velocity-time’ graph represent? What do positive and negative values of these slopes im ply? 15. How can one determine (i) the distance (ii) the displacement covered by a uniformly acceler-

ated body from its velocity-time graph? 16. Figure shows the x coordinate of a particle as a function of time. Find the signs of v x and a x

at t =t 1, t =t 2 and t =t 3. x

DISPLACEMENT

B

60°

O

4.

A

30° TIME

What will be nature of velocity-time graph for a uniform motion?

5.

What will be the nature of position-time graph for a uniform motion?

6.

What does slope of position-time graph represent for a uniform motion?

7.

If the displacement-time graph of a particle is parallel to (a) displacement axis (b) the time axis, what will be the velocity of the particle?

8.

Can position-time graph have negative slope?

9.

Draw position - time graph for a stationary object.

10. The displacement-time graph for the two par-

ticles A and B are straight lines inclined at

Page # 22

17. The velocity-time graph of a body moving in a straight line is shown in fig. Find the displace-

ment and the distance travelled by the body in 6 seconds.

18. The velocity-time graph of a particle moving

along a straight line is as shown in fig. Calculate the distance covered between t =0 to t =10 seconds. Also find displacement in time 0 to 10 seconds.


Master Your Physics - NEET / AIIMS v

KINEMATICS -1

OA, AB, BC, CD

( m/s)

20 10 0

(A) +

0

+

+ (B) – 0

+

0

(C) +

0

–

+(D) – 0

–

0

t(s) 2

4

8

6

22.

10

-10

The displacement-time graph of moving particle is shown below

-20 s


19. The velocity-time graph of a particle moving

along a straight line is shown in the fig. by curve OABCD. Calculate the distance di stance covered by the particle particle between between (i) t =zero =zero to t =18 =18 seconds (ii (ii)) t = 2 s to t to t = 12 s. s. and the maximum value of acceleration during this interval. v

(m/s)

A

20 15

F E

C

Time

t

The instantaneous velocity of the particle is negative at the point (A) D (A) D

(B) F (B) F

(C) C

(D) E (D) E

23. Which of the following velocity-time velocit y-time graphs shows a realistic situation for a body in motion

C

B

10

D

5

D

O 2

4

6

8

10

12

14

16

v

v

t(s)

18

(A)

(B)

20. Mark the correct statements for a particle

t

t

going on a straight line: (A) If the velocity and acceleration have opposite sign, the object is slowing down. (B) If the position and velocity velocity have opposite opposite sign, the particle is moving towards the origin. ori gin. (C) If the velocity velocity is zero at an instant, the acceleration should also be zero at that instant. (D) If the velocity is zero zero for a time interval, the acceleration is zero at any instant within the time interval.

v

v

(C)

(D) t

t

24. Figure shows the displacement-time displacement-time graph of

a particle moving on the X-axis.

21. The graph between the displacement x and time t for a particle moving in a straight line is shown in figure. During the interval OA, AB, BC and CD ,

the acceleration of the

particle is (A) the particle is continuously going in positive x tive x direction direction

Y


(B) the particle is at rest

D

A

B

O

X

Time t

Page # 23

C

(C) the velocity increases up to a time t0, and then becomes constant (D) the particle moves at a constant velocity up to a time t0, and then stops.



KINEMATICS -1

25. The velocity-time plot for a particle moving

on a straight line is shown in the t he figure.

29. Figure shows the graph of the x-coordinate of

(A) The particle has a constant acceleration. (B) The particle has never turned around. (C) The particle has zero displacement. (D) The average speed in the interval 0 to 10 s is the same as the average speed in the interval inter val 10 s to 20 s.

a particle going along the X-axis as a function of time. Find (a) the average velocity duri ng 0 to 10 s, (b) instantaneous velocity at 2, 5, 8 and 12s.

26. Figure shows the position of a particle part icle moving

on the X-axis as a function of time.

30. From the velocity-time plot shown in figure, f igure,

find the distance travelled by the particle during the first 40 seconds. Also find the average velocity during this period.

(A) The particle has come to rest 6 times. (B) The maximum maximum speed speed is at t = 6 s. (C) The velocity remains positive for t - 0 to t = 6 s. (D) The average velocity for the total period shown is negative. 27. The speed of a car as a function of time is

shown in figure. Find the distance travelled by the car car in 8 seconds and its acceleration.

31. A particle starts from a point A and travels along the solid curve shown in figure. Find

approximately the position B position B of the particle such that the average velocity between the positions A positions A and B and B has the same direction as the instantaneous velocity at B. at B.

28. Figure shows the graph of velocity versus time

for a particle going along the X-axis. Find (a) the acceleration, (b) the distance travelled in 0 to 10s and (c) the displacement in 0 to 10 s.

Page # 24

32. The variation of velocity of a particle with time

moving along a straight line is illustrated in the following figure. The distance travelled



KINEMATICS -1

by the particle in four seconds is  (m/s)

4 3

)

30

2

y t i c o l e V

20

1

s / m (

0

10

t (sec)

0

1 2 3 Time in second

(A) 60 m

(B) 55

(C) 25

(D) 30

4

(A) 60 m

(B) 50 m

(C) 30 m

(D) 40 m

36. For the velocity-time graph shown in figure

33. The v  t graph of a moving object is given in figure. The maximum acceleration is

)

10 20 30 40 50 60

below the distance covered covered by the body in last two seconds of its motion is what fraction of the total distance covered by it in all the t he seven seconds

80

c e s 60 / m c (

10 )

c e s 8 / m ( 6

y 40 t i c o l e 20 V

0

10

20

30 40 50 60 70 Time (sec.)

y t i c o l e V

80

4 2 1

(A) 1cm / sec c 3 cm / sec 2

2

(B) 2cm / sec ( 2

C

)

(D) 6 cm / sec 2

3 4 5 Time (sec)

6

(A)

1 2

(B)

1 4

(C)

1 3

(D)

2 3

34. A lift is going up. The variation in the speed

of the lift is as given in the graph. What is the height to which the lif t takes the passengers

2

7

)

c e s / m ( y t i c o l e V

3.6

2

(A) 3.6 m

Time (sec )

10

12

(B) 28.8

(C) 36.0 m (D) Cannot be calculated from the above graph 35. Velocity-time (v-t (v-t ) graph for a moving object is shown in t he figure. Total displacement of

the object during the t ime interval when there is non-zero acceleration and retardation is

Page # 25



KINEMATICS -1

Practice Problem - 6 Objective Questions 1.

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The

100

s r u o 80 h / m 60 k n 40 i d e 20 e p S

displacement ( s)  velocity (v) graph of this object is

A

s

s

(A)

(B) v

v

4. s

s

(C)

B

C

N

M

L

0.25 0.75 1.00

E

1.5 Time in hours

(A) 140 km h –2

(B) 160 km h –2

(C) 100 km h –2

(D) 120 km h –2

2.00

Acceleration-time graph of a body is shown. The corresponding velocity-time graph of the same body is

(C) a

v

v

2.

D

The graph of displacement v/ s time is t s v

v

t

(A)

(B)

Its corresponding velocity-time graph will be

t

(A)

v

v

v

v

(C)

(C)

(D) t

t

t

t

t

5.

The acceleration-time graph of a body is shown below

v

v

a

(C)

(D) t

3.

t

A train moves from one station to another in 2 hours time. Its speed-time graph during this motion is shown in the figure. The maximum acceleration during the journey is

Page # 26

t

The most probable velocity-time graph of the body is


Master Your Physics - NEET / AIIMS 



(A)

(A)

(B)

(C)

m/ s

3

(B) 3 m/ s

3 m/ s

(D)

t

t

7. 



(C)

1

KINEMATICS -1

(D)

The   t plot of a moving object is shown in the figure. The average velocity of the object during the first 10 seconds is

)

5

1 -

t

t

6.

From the following displacement-time graph find out the velocity of a moving body

)

c e

s ( e m i T

30

1 3

s

m ( y t i c 0 o l e V

Time (sec) 5

10

– 5

(A) 0

(B) 2.5 ms –1

(C) 5 ms –1

(D) 2 ms –1 ****

o

O Displacement (meter)

10. UNIFORMLY ACCELERATED MOTION If a particle is accelerated with constant acceleration in an interval of time, then the motion is termed as uniformly accelerated motion in that interval of time. For uniformly accelerated motion along a straight li ne (xaxis) during a time interval of t seconds, the following important results can be used. (a)

v = u + at

(b)

s = ut + 1/2 at2 s = vt  1/2 at2 xf = xi + ut + 1/2 at 2

(c)

v2 = u2 + 2as

(d)

s = 1/2 (u + v) t

(e)

sn = u + a/2 (2n  1)

u = initial velocity (at the beginning of interval) a = acceleration v = final velocity (at the end of interval) s = displacement (xf  xi) xf = final coordinate (position) xi = initial coordinate (position) sn = displacement during the nth sec

Page # 27



KINEMATICS -1

Example 13. A particle moving rectilinearly with constant acceleration is having initial velocity of 10 m/s. After some time, its velocity becomes 30 m/s. Find out velocity of the particle at the mid point of its path? Sol. Let the total distance be 2x.

 distance upto midpoint = x Let the velocity at the mid point be v and acceleration be a. From equations of motion v2 = 102 + 2ax

____ (1)

302 = v2 + 2ax

____ (2)

(2) - (1) gives



v2 - 302 = 102 - v2



v2 = 500

v = 10 5 m/s

Example 14.

A police inspector in a jeep is chasing a pickpocket an a straight road. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the j eep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pick pocket will be caught if v 

2ad .

Sol. Suppose the pickpocket is caught at a time t after motorcycle starts. The distance travelled by the motorcycle during this interval is

s

1 2

at2

____ (1)

During this interval the jeep travels a distance

s  d  vt

____ (2)

1

By (1) and (2),

2 t

or,

at 2



 d  vt

v  v2

 2ad

a

The pickpocket will be caught if t is real and positive. v2

This will be possible if

 2ad or,, v  2ad

Example 15.

The velocity acquired by a body moving with uniform acceleration is 20 m/s in first 2 sec and 40 m/s in first 4 sec. Calculate initial velocity.

Sol.

u

 v1 a t 2  t1 v2

a

t=0

v1 t1 = 2 sec

v2 t2 = 4 sec

40  20 20   10 m / s 2 42 2

Now,

v

 u  at v1

Page # 28

 u  at1


Master Your Physics - NEET / AIIMS 

20  u  10  2



20  u  20



u  0m / s

KINEMATICS -1

Ans

Example 16.

A particle starts with initial velocity 2.5 m/s along the x direction and accelerates uniformly at the rate 50 cm/s2. Find time taken to increase the velocity to 7.5 m/s. u = 2.5 m/s

Sol. v

a = 0.5 m/s

2

v = 7.5 m/s

 u  at t= 0

t=?

7.5  2.5  0.5 t 5.0  0.5t

t

50 5

 10 sec

Example 17.

A particle starts with a constant acceleration. At a time t second speed is found to be 100 m/s and one second later speed becomes 150 m/s. Find acceleration of the particle. Sol. From equation (1) of motion v = u + at



100 = 0 + at 100 = at

... (1)

Now consider velocity one second later -

v'



 0  a  t  1

150  a  t  1

... (2)

On subtracting equation (1) from equation (2)

a  50 m/ s2 Example 18.

A truck starts from rest with an acceleration of 1.5 ms-2 while a car 150 metre behind starts from rest with an acceleration of 2 ms-2. (a) How long will it take before both the truck and car are side by side and (b) How much distance is travelled by each.

Sol. (a) sT

sT 

1 2

 at 2

1 1.5  t 2 .... (1) 2

Distance covered by car when car one overtakes the truck

Page # 29


Master Your Physics - NEET / AIIMS sc

KINEMATICS -1

1 2

  2 t 2 1 2

 sT  150    2 t 2

.... (2)

Divide equation (2) by equation (1)

150



sT



4 3

1

1

or

3

sT

 150 sT sT



2 1.5



1

150 sT



20 15



4 3

 450

Distance travelled by car = 450 + 150 = 600 metre (b) Now by equation (1) sT

450 

t2



450  2



1.5

t

1 2

 at 2 1  1.5  t 2 2

 300  2  24.5 sec

Therefore car will overtake the truck after 24.5 second. Example 19.

A body travels a distance of 20 m in the 7th second and 24 m in 9th second. How much distance shall it travel in the 15th second? Sol. Here,

s7 = 20 m ; s 9 = 24 m,

s15 = ? Let u and a be the initial velocity and uniform acceleration of the body. We know that, sn  u 

a  2n  1 2



s7  u 

a  2  7  1 2

or

20  u 

13a 2

and

s9

or

24 = u +

.... (i)

a

 u  (2  9  1) 2

7 2

a

....... (ii)

Subtracting (ii) form (i), we get 4 = 2a

or

a = 2 ms –2

Putting this value in (i), we get

Page # 30


Master Your Physics - NEET / AIIMS 20  u 

13 2 2

KINEMATICS -1

or 20 = u + 13

u = 20 – 13 = 7 ms –1

or

Hence, s15 = u 

a 2 (2 × 15 – 1) = 7 + × 29 2 2

s15 = 36 m

Ans.

Example 20.

A person travelling at 43.2 km/h applies the brakes giving a deceleration of 6 m/s 2 to his scooter. How far will it travel before stopping? Sol. Here, u  43.2 km / h = 43.2 

Deceleration;

a = 6 m/s2

5 m/s 18 v = 0 s = ?

0 = (12)2 – 2 x 6 s

s

144 12

Using

v2 = u2 - 2as

144 = 2 x 6s

 12m

Ans.

Example 21.

A bullet going with speed 350 m/s enters in a concrete wall and penetrates a distance of 5 cm before coming to rest. Find deceleration. Sol. Here,

By using

u = 350 m/s,

s = 5 cm, v = 0 m/s

0  u2 2

u

Page # 31

5cm

 2as

 2as or

a=

a = ? u = 350 m/s

 u2  2as

v2

and

350  350 2  0.05

a

u2 2s

= 12.25 × 105 m/sec2



KINEMATICS -1


2.

3.

4.

A particle starts moving from position of rest under a constant acceleration. If it travels a distance x in t second, what distance will it travel in next t second ? –1

A car travelling at 72 km h takes a U turn in 10 seconds. What is the acceleration of the car ? A body starting from rest has an acceleration of 20 ms –2. Calculate the distance travelled by it in 6th second. A train was moving at a rate of 36 km h –1. When the brakes were applied, it comes to rest in a distance of 200 m. Calculate the retardation produced in the train.

5.

A body covers 12 m in 2nd second and 20 m in 4th second. Find what distance the body will cover in 4 seconds after the 5th second.

6.

On turning a corner, a motorist rushing at 44 ms –1 finds a child on the road 100 m ahead. He instantly stops the engine and applies the brakes so as to stop it within 1 m of the child. Calculate time required to stop it.

7.

8.

9.

A body starting from rest, was observed to cover 20 m in 1 second and 40 m during the next second. How far had it travelled before the first observation was taken ? An automobile starts from rest and accelerates uniformly for 30 second to a speed of 72 km h –1. It then moves with a uniform velocity and it is finally brought to rest in 50 m with a constant retardation. If the total distance travelled is 950 m, find the acceleration, the retardation and total time taken. A particle starts from rest with a constant acceleration. At a time t second, the speed is found to be 100 m/s and one second later the speed becomes 150 m/s. Find (a) the acceleration and (b) the distance travelled during the (t + 1) th second.

10. A police inspector in a jeep in chasing a pick-

pocket on a straight road. The jeep is going at its maximum speed  (assumed uniform). The

Page # 32

pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pickpocket will be caught if v  2ad . 11. An object having a velocity 4.0 m/s is acceler-

ated at the rate of 1.2 m/s2 for 5.0 s. Find the distance travelled during the period of acceleration. 12. A person travelling at 43.2 km/h applies the

brake giving a deceleration of 6.0 m/s2 to his scooter. How far will it travel before stopping ? 13. A train starts from rest and moves with a constant acceleration of 2.0 m/s2 for half a minute.

The brakes are then applied and the train comes to rest in one minute. Find (a) the total distance moved by the train, (b) the maximum speed attained by the train and (c) the position(s) of the train at half the maximum speed. 14. A particle starting from rest moves with con-

stant acceleration. If it takes 5.0s to reach the speed 18.0 km/h find (a) the average velocity during this period and (b) the distance travelled by the particle during this period. 15. A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at

a speed of 72 km/h. The jeep follows it at a speed of 90 km/h, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike ?

16. A particle experiences a constant acceleration for 20 sec after starting from rest. If it travels

a distance S1 in the first 10 sec and a distance S2 in the next 10 sec, then

(A) S1  S2

(B) S1  S2 / 3

(C) S1  S2 / 2

(D) S1  S2 / 4



KINEMATICS -1

17. A point moves with uniform acceleration and

and B starts in the same direction with constant

v1 , v 2 and v 3 denote the average velocities in

acceleration of 4 m / s 2 , then B will catch A

the three successive intervals of time t 1 , t 2 and

after how much time

t 3 . Which of the following relations is correct

(A) 10 sec

(B) 20 sec

(C) 30 sec

(D) 35 sec

(A) (v1  v 2 ) : (v 2  v 3 )  (t 1  t 2 ) : (t 2  t 3 )

22. The average velocity of a body moving with

(B) (v1  v 2 ) : (v 2  v 3 )  (t 1  t 2 ) : (t 2  t 3 )

uniform acceleration travelling a distance of 3.06 m is 0.34 ms –1. If the change in velocity of the body is 0.18ms –1 during this time, its uniform acceleration is

(C) (v1  v 2 ) : (v 2  v 3 )  (t 1  t 2 ) : (t 1  t 3 ) (D) (v1  v 2 ) : (v 2  v 3 )  (t 1  t 2 ) : (t 2  t 3 ) 18. The initial velocity of the particle is 10 m / sec

(A) 0.01 ms –2

(B) 0.02 ms –2

and its retardation is 2m / sec 2 . The distance

(C) 0.03 ms –2

(D) 0.04 ms –2

moved by the particle in 5th second of its motion is (A) 1 m (B) 19 m

(C) 50 m

(D) 75 m

19. The velocity of a body moving with a uniform

acceleration of 2 m. / sec

2

is

10 m / sec

. Its

velocity after an interval of 4 sec is (A) 12 m / sec

(B) 14 m / sec

(C) 16 m / sec

(D) 18 m / sec

23. A particle starts from rest, accelerates at 2 m/

s2 for 10 s and then goes for constant speed for 30 s and then decelerates at 4 m/ s2 till it stops. What is the distance travelled by it (A) 750 m

(B) 800 m

(C) 700 m

(D) 850 m

24. A car, starting from rest, accelerates at the

rate f through a distance S , then continues at constant speed for time t and then decelerates

20. Two cars A and B are travelling in the same

direction with velocities v1 and v 2 (v1  v 2 ) . When the car is at a distance ahead of the car , the driver of the car applied the brake producing a uniform retardation There will be no collision when

at the rate

(A) d 

(C) d 

2a (v1  v 2 ) 2a

(B) d 

2

(D) d 

v12  v 22 2a 2 1

v

v

2 2

2a

21. Two cars A and B at rest at same point initially.

If A starts with uniform velocity of 40 m/sec

Page # 33

2

to come to rest. If the total

distance traversed is 15 S , then 1 2

(B) S 

1 2 ft 72

2 (D) S  ft

2 (A) S  ft

(C) S 

(v1  v 2 ) 2

f

1 2 ft 4 1 6

25. A man is 45 m behind the bus when the bus

start accelerating from rest with acceleration 2.5 m/s2. With what minimum velocity should the man start running to catch the bus ? (A) 12 m/s

(B) 14 m/s

(C) 15 m/s

(D) 16 m/s



KINEMATICS -1

MOTION UNDER GRAVITY

The most important example of motion in a straight line with constant acceleration is motion under gravity. In case of motion under gravity. (1) The acceleration is constant, i.e., a = g = 9.8 m/s 2 and directed vertically downwards. (2) The motion is in vacuum, i.e., viscous force or thrust of the medium has no effect on the motion. [1] Body falling freely under gravity :

Taking initial position as origin and downward direction of motion as positive, we have u = 0

[as body starts from rest]

a=– g

[as acceleration is in the downward direction]

So, if the body acquires velocity v after falling a distance h in time t, equations of motion, viz. v = u + at;

s  ut 

1 2 at 2

v = –gt ... (1) h 

reduces to

and

1 2

v2

gt 2 ..... (2)

 u2  2as

and

v2

 2gh ..... (3)

These equations can be used to solve most of the problems of freely falling bodies as if.

t is given

h is given

v is given

From eqns. (1) and (2) and (1)

From eqns. (2) and (3)

From Eqns. (3)

v = –gt

t

and h 

(i)

1 2

gt

2

2h g

t



h

v  2gh

v g

v 2 2g

If the body is dropped from a height H, as in time t is has fallen a distance h from its initial position,

 1

' 2 the height of the body from the ground will be h  H  h with h    gt  2

Page # 34


Master Your Physics - NEET / AIIMS (ii)

KINEMATICS -1

 1 2 As h     gt , i.e., h  t 2 , distance fallen in time, t,2t,3t etc., will be in the ratio of 12 : 22 : 32, 2 i.e., square of integers.

(iii)

The distance fallen in the nth sec, hn

1 2

2

1 2

 h n1  g  n  g  n  1

1 2

2

 g  2n  1

So distances fallen in 1st, 2nd, 3rd sec etc. will be in the ratio of 1 : 3 : 5 i.e., odd integers only. [2]

Body projected vertically up :

Taking initial position as origin and direction of motion (i.e., vertically up) as positive. here we have

v = 0 [at highest point velocity = 0] a = – g[as acceleration is downwards while motion upwards]

If the body is projected with velocity u and reaches the highest point at a distance h above the ground in time t, the equations of motion viz., s  ut 

v = u + at;

reduces to

1 2 at 2

and

h  ut 

0 = u – gt

1 2 gt 2

v2

 u2  2as

and

0 = u2 – 2gh

Substituting the value of u from first equation in second and rearranging these, u = gt

...

(1)

1 2 gt 2

...

(2)

 2gh

...

(3)

h u2

and

These equations can be used to solve most of the problems of bodies projected vertically up as if.

t is given From eqns. (1) and (2)

From eqns. (2) and (3) t

u = gt

and h 

h is given

1 2 gt 2

(A)

Page # 35



2h g

v  2gh

(B)

u is given From Eqns. (3) and (1) t



h

u g

u2 2g

(C)



KINEMATICS -1

IMPORTANT POINTS

(1)

In case of motion under gravity for a given body, mass, acceleration, and mechanical energy remain constant while speed, velocity, momentum, kinetic energy and potential energy change.

(2)

The motion is independent of the mass of the body, as in any equation of motion, mass is not involved. This is why a heavy and lighter body when released from the same height, reach the ground simultaneousl y and with same velocity. t

i.e

  2h / g and v  2gh

However, momentum, kinetic energy or potential energy depend on the mass of the body (all  mass) (3)

As from equation (2) time taken to reach a height h, tu

  2h / g

Similarly, time taken to fall down through a distance h,

so

tD

  2h / g

tu

 tD   2h / g 

So in case of motion under gravity time taken to go up a height h is equal to the time taken to fall down through the same height h. (4)

If a body is projectd vertically up and it reaches a height h, then u

 2gh

and if a body falls freely through a height h, then v

  2gh   u

So in case of motion under gravity, the speed with which a body is projected up is equal to the speed with which it comes back to the point of projection. Example 22.

A juggler throws balls into air. He throws one whenever the previous one is at its highest point. How high do the balls rise if he throws n balls each sec. Acceleration due to gravity is g. Sol. Since the juggler is throwing n balls each second and he throws second ball when the first ball is at the highest point, so time taken by each ball to reach the highest point is t = 1/n

Taking vertical upward motion of ball up to the highest point, we have u = 0, a = – g, t = 1/n, u = ? As

v = u + at

so

0 = 0 u + (–g) 1/n

or

u = g/n

Also

v2 = u2 + 2as,

so

0 = u2 – 2gh

i.e.,

h = (u2/2g) = g/(2n2)

Example 23.

A ball is projected vertically up with an initial speed of 20 m/s on a planet where acceleration due to gravity is 10 m/s2.

Page # 36



KINEMATICS -1

(a) How long does it takes to reach the highest point? (b) How high does it rise above the point of projection? (c) How long will it take for the ball to reach a point 10 m above the point of projection? Sol. As here motion is vertically upwards,

a = –g and v = 0 (a) From 1st equation of motion, i.e., v = u + at, 0 = 20 – 10t i.e.

t = 2 sec.

2

Ans.

2

(b) Using v = u + 2as 0 = (20)2 – 2 x 10 x h i.e

h = 20 m. s  ut 

(c) Using

Ans.

1 2 at , 2

1 2

10 = 20t (– ) x 10 x t2

i.e.

t2 – 4t + 2 = 0

i.e.

t = 0.59 sec. or 3.41 sec.

or

t

 2 2 ,

i.e., there are two times, at which the ball passes through h = 10 m, once while going up and then coming down. Example 24.

A ball is thrown vertically upwards from a bridge with an initial velocity of 4.9 m/s. It strikes the water after 2s. If acceleration due to gravity is 9.8 m/s2 (a) What is the height of the bridge? (b) With which velocity does the ball strike the water? Sol. Taking the point of projection as origin and downward direction as positive,

 1 s  ut    at 2 we have 2

(a) Using

 1  9.8  22  9.8m (u is taken to be negative as it is upwards)  2

h  4.9  2  

(b) Using

v = u + at v = –4.9 + 9.8 x 2 = 14.7 m/s

Example 25.

A body is released from a height and falls freely towards the earth. Exactly 1 sec later another body is released. What is the distance between the two bodies after 2 sec the release of the second body, if g = 9.8 m/s2. h2

Sol. The 2nd body falls for 2s, so

1 2

 g  2

2

...

(1)

While 1st has fallen for 2 + 1 = 3 sec so h1

1 2

 g 3

2

...

(2)

 Separation between two bodies after 2 sec the release of 2nd body,, d  h1  h2

1 2

 g  3 2  22 

 4.9  5  24.5m

Example 26.

If a body travels half its total path in the last second of its fall from rest, find : (a) The time and (b) height of its fall. Explain the physically unacceptable solution of the quadratic time equation. (g

Page # 37



KINEMATICS -1

= 9.8 m/s2) Sol. If the body falls a height h in time t, then h

1 2 gt 2

[ u = 0 as the body starts from rest]

... (1)

Now, as the distance covered in (t – 1) second is h’ 

1 2 g  t  1 2

... (2)

So from Equations (1) and (2) distance travelled in the last second. h – h’

i.e.,

1 2 gt 2

1 2

2

 g  t  1

h – h’ 

1 g  2t  1 2

But according to given problem as (h –h’) 

i.e.,

 1  1   h    g  2t  1  2  2

or

 1 2  2  gt  g  2t  1  

or

t2

Page # 38

h 2

1 [as from equation (1) h    gt 2 ] 2

 4t  2  0



KINEMATICS -1

Practice Problem - 8 Theoretical Questions 1.

A stone is thrown vertically upwards from the surface of earth. What is the direction of the velocity and acceleration of the stone (a) on its way up (b) on its way down.

2.

A man standing on the edge of a cliff throws a stone straight up with initial speed u and then throws another stone stright down with same initial speed and from the same position. Find the ratio of the speeds, the stones would have attained when they hit ground at the base of the cliff.

3.

Two balls of different masses (one lighter and with the same speed. Which one will pass through the point of projection in their downward direction with the greater speed? A ball is dropped from the roof of a tower of height h. The total distance covered by it in the last second of its motion is equal to the distance covered by it in first three seconds. What is the value of h? ( g = 10m/s2)

5.

A ball is thrown vertically upwards with a velocity of 20 ms-1 from the top of a multi-storey building. The height of the point from where the ball is thrown is25. 0 m from the ground. (a) How high the ball will rise? and (b) how long will it be before the ball hits the ground? Take, g = 10 ms-2.

6.

A stone is dropped from the top of a cliff and is found to travel 44.1 m in the last second before it reaches the ground. Find the height of the cliff.

7.

velocity was it thrown? How far below its highest point was in 3 second after start? Acceleration due to gravity is 9.8 ms –2. From top of a tower 200 m in height, a ball is dropped and at the same time another ball is projected vertically upwards from the ground –1

with a velocity of 50 ms . Find when and where the two balls will meet.

Page # 39

is dropped and at the same instant another ball is projecred vertically upwards from the ground so that it just reaches the top of tower. At what heigh do the two balls pass one another? 10. A body falling from rest was observed to fall

through 78.4 m in 2 seconds. Find how long had it been falling before it was observed? 11. A stone is dropped from a balloon going up

with a uniform velocity of 5.0 m/s. If the baldropped, find its height when the stone hits the ground. Take g = 10 m/s2. 12. Aball is thrown vertically upward with a speed

of 20 m/s. Draw a graph showing the velocity of the ball as a function of time as it goes up and then comes back. 13. A ball is projected vertically upward with a

speed of 50 m/s. Find (a) the maximum height, (b) the time to reach the maximum height, (c) the speed at half the maximum height. Take g = 10 m/s 14. A stone is thrown vertically upward with a

speed of 28 m/s. (a) Find the maximum height reached by the stone. (b) Find its velocity one second before it reaches the maximum height. (c) Does the answer of part. (d) change if the initial speed is more than 28 m/s such as 40 m/s or 80 m/s? 15. A person sitting on the top of a tall building is

dropping balls at regular intervals of one second. Find the positions of the 3rd, 4th and 5th

A ball thrown up is caught by the thrower after 4 second. How high did it go and with what

8.

From the top of a tower 100 m in height a ball

loon was 50 m high when the stone was

other heavier) are thrown vertically upwards

4.

9.

ball when the 6th ball is being dropped. 16. A ball is dropped from a height. If it takes 0.200

s to cross the last 6.00 m before hitting the ground, find the height from which it was dropped. Take g = 10 m/s2.

Objective Questions 17. A stone falls from a balloon that is descending

at a uniform rate of 12 m / s . The displacement of the stone from the point of release after 10 sec is



19.

20.

21.

22.

23.

24.

25.

(A) 490 m (B) 510 m (C) 610 m (D) 725 m A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is (A) 2100 m/sec2 downwards (B) 2100 m/sec2 upwards (C) 1400 m/sec2 (D) 700 m/sec2 A body A is projected upwards with a velocity of 98 m/ s The second body B is projected upwards with the same initial velocity but after 4 sec. Both the bodies will meet after (A) 6 sec (B) 8 sec (C) 10 sec (D) 12 sec A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of (A) 3 s (B) 5 s (C) 7 s (D) 9 s A stone is dropped into water from a bridge 44.1 m above the water. Another stone is thrown vertically downward 1 sec later. Both strike the water simultaneously. What was the initial speed of the second stone (A) 12.25 m / s (B) 14.75 m / s (C) 16.23 m / s (D) 17.15 m / s A body is released from a great height and falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies, two seconds after the release of the second body is (A) 4.9 m (B) 9.8 m (C) 19.6 m (D) 24.5 m An object is projected upwards with a velocity of 100 m / s . It will strike the ground after (approximately) (A) 10 sec (B) 20 sec (C) 15 sec (D) 5 sec A stone dropped from the top of the tower touches the ground in 4 sec. The height of the tower is about (A) 80 m (B) 40 m (C) 20 m (D) 160 m A man in a balloon rising vertically with an acceleration of 4.9 m / sec 2 releases a ball 2 sec after the balloon is let go from the ground. The greatest height above the ground reached by the ball is ( g  9.8 m / sec 2 ) (A) 14.7 m (B) 19.6 m (C) 9.8 m (D) 24.5 m

Page # 40

KINEMATICS -1

26. Water drops fall at regular intervals from a tap

27.

28.

29.

30.

31.

32.

which is 5 m above the ground. The third drop is leaving the tap at the instant the first drop touches the ground. How far above the ground is the second drop at that instant (A) 2.50 m (B) 3.75 m (C) 4.00 m (D)1.25 m A body starts to fall fr eely under gravity. The distances covered by it in first, second and third second are in ratio (A) 1 : 3 : 5 (B) 1 : 2 : 3 (C) 1 : 4 : 9 (D) 1 : 5 : 6 A body is projected up with a speed ' u' and the time taken by it is T to reach the maximum height H . Pick out the correct statement (A) It reaches H / 2 in T / 2 sec (B) It acquires velocity u / 2 in T / 2 sec (C) Its velocity is at (D) Same velocity at A body is thrown vertically upwards with a velocity u . Find the true statement from the following (A) Both velocity and acceleration are zero at its highest point (B) Velocity is maximum and acceleration is zero at the highest point (C) Velocity is maximum and acceleration is g downwards at its highest point (D) Velocity is zero at the highest point and maximum height reached is u2/2g Two balls A and B of same masses are thrown from the top of the building. A, thrown upward with velocity V and B, thrown downward with velocity V , then (A) Velocity of A is more than B at the ground (B) Velocity of B is more than A at the ground (C) Both A & B strike the ground with same velocity (D) None of these A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 m/s2. He reaches the ground with a speed of 3 m/ s. At what height, did he bail out ? (A) 293 m (B) 111 m (C) 91 m (D) 182 m When a ball is thrown up vertically with velocity V o , it reaches a maximum height of ‘h’. If one wishes to triple the maximum height then the ball should be thrown with velocity (A) 3 V o (B) 3V o (C) 9 V o (D) 3 / 2V o



KINEMATICS -1

12. MOTION WITH NON-UNIFORM ACCELERATION (use of definite integrals) t f

 v( t )dt

x =

(displacement in time interval t = t i to tf )

ti

The expression on the right hand side is called the definite integral of v(t) between t = ti and t = tf . . Similarly change in velocity

v = vf  vi =

t f

 a(t)dt ti

Table : Some quantities defined as derivatives and integrals.

dx

v(t) =

a (t) =

dv

 dx =

v =

 dv = 

 p =

W=

dp =

a = slope of vt graphs

dt

F (t) =

x =

v = slope of xt graph

dt

dp

F = slope of pt graph (p = linear momentum)

dt

t f

 v ( t ) dt

x = area under vt graph

ti t f

 a ( t ) dt

v = area under a t graph

ti t f

 F ( t ) dt

 p = area under Ft graph

ti

 dW =

xf

 F (x) dx

W = area under Fx graph

xi

13. SOLVING PROBLEMS ACCELERATION

WHICH

INVOLVES

NON

UNIFORM

13.1 Acceleration depending on velocity v or time t dv By definition of acceleration, we have a = . If a is in terms of t, dt v

of v,

dv

v

t

v0

0

 dv =  a ( t ) dt . If a is in terms

 a (v )   dt . On integrating, we get a relation between v and t, and then

v0

x

t

0

using

 dx

x0

=

t

 v (t ) dt , x and t can also be related. 0

Page # 41



KINEMATICS -1

13.2 Acceleration depending on velocity v or position x

dv

a=



dt

a=

dv dx dx dt

 a=

dx dv

 a = v

dt dx

dv dx

This is another important expression for acceleration. v

x

v0

x0

 v dv =  a (x ) dx .

If a is in terms of x,

v



If a is in terms of v,

v0

x

v dv a( v )



 dx x0

x

On integrating, we get a relation between x and v. Using



x0

t

dx v (x ) =

 dt , we can relate x and t. 0

Example 27.

The displacement of a particle is given by y = a + bt + ct 2 + dt4. Find the acceleration of a particle. Sol.

v

dy d   a  bt  ct 2  dt 4   b  2ct  4dt 3 dt dt

a

dv dt

 2c  12dt2

Example 28.

If the displacement of a particle is (2t 2 + t + 5) meter then, what will be acceleration at t = 5 sec. Sol.

v

dx d  2t 2  t  5   4t  1 m / s and  dt dt

a

dv d   4t  1 a = 4 m/s2 dt dt

Example 29.

The velocity of a particle moving in the x direction varies as V   x where  is a constant. Assuming that at the moment t = 0 the particle was located at the point x = 0. Find the acceleration. Sol.

a

=

dv dt

.

 1

2 x

d 1 dx x   . x 1/ 2 . dt 2 dt . x



a

2 2

Example 30.

The velocity of any particle is related with its displacement As; x at x = 5 m. Sol.

x  v 1

Page # 42

x2

 v 1

v   x2

 v  1 , Calculate acceleration

 1


Master Your Physics - NEET / AIIMS Therefore a 

dv dt



d 2 x dt

 1  2x

dx dt

KINEMATICS -1

 2x v  2x  x 2  1

a  2  5  25  1  240 m / s2

at x = 5 m Example 31.

The velocity of a particle moving in the positive direction of x-axis varies as v =

 x where 

is positive constant. Assuming that at the moment t = 0, the particle was located at x = 0 find, (i) the time dependance of the velocity and the acceleration of the particle and (ii) the mean velocity of the particle averaged over the time that the particle takes to cover first s metres of the path. Sol. (i) Given that

dx



x

dx

v

  x or dt   x

  dt

dx

0

x

t

 0  dt

  t or x   2 t2 / 4

Hence

2 x

Velocity

dx 1 2   t and dt 2

Acceleration

x



or

d2 x dt 2

1 2

 2

(ii) Time taken to cover first s metres

s

v 

2 t2 4

t2

or

total dis tan ce s = total time 2 s



4s



t

or

2

or

v



2 s

1 s 2

 

Example 32.

A particle moves in the plane xy with constant acceleration a directed along the negative y-axis. The equation of motion of the particle has the form y = px – qx 2 where p and q are positive constants. Find the velocity of the partcle at the origin of coordinates. Sol. Given that y = px – qx2



d2 y d2 x d2 x dy dx dx  dx     2q   p 2qx p  q.2x and 2 2 2 dt dt dt dx dt dt  dt 

or

 dx  a  2q     2q 2x  dt 

2

2



d2 x dt 2

Page # 43

 0 (no acceleration along x-axis) and

d2 y dt 2

 a


Master Your Physics - NEET / AIIMS 

2x 

2q

a

x 

or

 dy   p dx  dt  dt   x0

Further,



a

KINEMATICS -1

2q

 y  p x

or

 a y  p    2q 

Now





2 x



2 y



 a ap2       2q 2q 

or

 a  p2  1      2q 

Ans.

SUMMARY Rectilinear Motion : Rectilinear motion is motion, along a straight line or in one dimension. Displacement : The vector joining the initial position of the particle to its final position during an

interval of time. Distance : The length of the actual path travelled by a particle during a given time interval

Average Velocity =

Average Speed =

x f  x i displaceme nt = t f  t i time int erval

distance travelled time interval

 x  dx  =  t  dt

 Instantaneous Velocity : Vinst. = lim t 0 Average Acceleration

=

v f  v i change in velocity = time int erval t f  t i

Instantaneous Acceleration :

a=

dv

 v 

 = lim  t0  t  dt

Equations of Motion

(a)

v = u + at

(b)

s = ut + 1/2 at2 s = vt  1/2 at2 xf = xi + ut + 1/2 at 2

(c)

Page # 44

v2 = u2 + 2as


Master Your Physics - NEET / AIIMS (d)

s = 1/2 (u + v) t

(e)

sn = u + a/2 (2n  1)

KINEMATICS -1

Important Points to Remember



For uniformly accelerated motion (a  0), xt graph is a parabola (opening upwards if a > 0 and opening downwards if a < 0). The slope of tangent at any point of the parabo la gives the velocity at that instant.



For uniformly accelerated motion (a  0), vt graph is a straight line whose slope gives the acceleration of the particle.



In general, the slope of tangent in xt graph is velocity and the slope of tangent in vt graph is the acceleration.



The area under a t graph gives the change in velocity.



The area between the vt graph gives the distance travelled by the particle, if we take all areas as positive. Area under vt graph gives displacement, if areas below the taxis are taken negative.



Maxima and Minima

Conditions for maxima are:

dy dx

= 0 (b)

d2 y

<0

dx 2

Conditions for minima are:

dy dx

= 0(b)

d2 y dx 2

>0

Motion with Non-Uniform Acceleration

x =

t f

 v( t )dt

v = vf  vi =

ti

t f

 a(t)dt ti

Solving Problems which Involves Nonuniform Acceleration v

If a is in terms of t,



t

dv =

v0 v




v0

If a is in terms of x,

0

dv a (v )



 dt 0

x

v0

x0

 v dv =  a (x ) dx .



v0

Page # 45

t

v

v


 a (t) dt

v dv a( v )

x



 dx x0



KINEMATICS -1

Practice Problem - 9 Theoretical Questions 1.

2.

3.

4.

5.

6.

7.

The displacement of a body as a function of time is given by s = (3t2 + 4t + 7) m. Calculate the magnitude of its instantaneous velocity and acceleration at t = 1 s. The acceleration of a particle varies with time t-seconds according to the relation a=6t+6 m/ s2. Find the velocity and position as a function of time. It is given that the particle starts from origin at t=0 with velocity 2 ms-1. At t=0 a body is started from origin with some initial velocity. The displacement x(m) of the body varies with time t(s) as x=-(2/3)t2+16t+2. Find the initial velocity of the body and also find how long does the body take to come to rest? What is the acceleration of the body when it comes to rest? The position x of a particle varies with time t according to the relation x=t3 +3t2+2t. Find velocity and acceleration as a function of time. The displacement of a particle along x-axis is given by x=3+8t+7t2. Obtain its velocity and acceleration at t= 2s. The acceleration a in ms-2 of a particle is given by a= 3t2+2t=2, where t is the time. If the particle starts out with a velocity v=2 ms-1 at t=0, then find the velocity at the end of 2 s. The displacement x of a particle along the xaxis at time t is given by x=

a1

2

t



a2

3

2.

t

Find

the acceleration of the particle. 8. A particle moves along a straight line such that its displacement s at any time t is given by s= t3-6t2+3t+4m, t being in seconds. Find the velocity of the particle when the acceleration is zero. Objective Questions 9. The displacement of a particle is given by

 dt 4 . The initial velocity and acceleration are respectively (A) b, -4d (B)-b, 2c (C) b,2c (D)2c, -4d 10. The acceleration ‘a’ in m/s2 of a particle is given by a=3t2 + 2t + 2 where t is the time. If the particle starts out with a velocity u = 2m/s at t = 0, then the velocity at the end of 2 second is y  a  bt  ct 2

Page # 46

(A) 12 m/s (B) 18 m/s (C) 27 m/s(D) 36 m/s 11. A particle moves along a straight line such that its displacement at any time t is given by S = t3 – 6t2 + 3t + 4 metres The velocity when the acceleration is zero is (A) 3 ms-1 (B) –12 ms-1 (C) 42 ms-1 (D) –9 ms-1 12. The displacement is given by x = 2t2 + t + 5, the acceleration at t = 2s is (A) 4 m/s2 (B) 8m/s2 (C) 10m/s2 (D) 15m/s2 13. The position x of a particle varies with time t as x = at 2 – bt 3 . The acceleration of the particle will be zero at time equal to (A)

a b

(B)

2a 3b

(C)

a 3b

(D)Zero

14. Equation of displacement for any particle is s =(3t 3+7t 2+14t+8)m. Its acceleration at time t = 1 sec is (A) 10 m/s2 (B) 16 m/s2 (C) 25 m/s2 (D) 32 m/s2 15. The motion of a particle is described by the equation x = a+bt 2 where a = 15 cm and b = 3 cm/s2. Its instantaneous velocity at time 3 sec will be (A) 36 cm/sec (B) 18 cm/sec ( C) 1 6 cm/sec (D) 32 cm/sec 16. A body is moving according to the equation x=at+bt 2 – ct 3 where x = displacement and a,b and c are constants. The acceleration of the body is (A) a+ 2bt (B) 2b+6ct (C) 2b-6ct (D) 3b-6ct2 17. The displacement of a particle, moving in a straight line, is given by s=2t 2+2t+4 where s is in metres and t in seconds. The acceleration of the particle is (A) 2 m/s2 (B) 4 m/s2 (C) 6 m/s2 (D) 8 m/s2 18. A particle moves along X-axis in such a way that its coordinate X varies with time t according to the equation x = (2 - 5t + 6t 2 ) m. The initial velocity of the particle is (A) –5m/s (B) 6 m/s (C) -3 m/s (D) 3 m/s 19. A particle moves along x-axis as x = 4 (t - 2) + a ( t - 2 )2 Which of the following is true ? (A) The initial velocity of particle is 4 (B) The acceleration of particle is 2a (C) The particle is at origin at t = 0 (D) None of these



KINEMATICS -1

Mock Test-1 Time : 3 hrs.

M. M. : 70

(One Mark Problems ) 1. Write the expression for distance covered in nth second by a uniformly accelerated body. 2. The position–time ( x – t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in figure. Choose the correct entries in the brackets below :

10. A jet airplane travelling at the speed of 500 kmh – 1 ejects its products of combustion at the speed of 1500 kmh –1 relative to the jet plane. What is the speed of the latter with respect to an observer on the ground ? 11. Adjoining figure shows the x – t plot of one dimensional motion of a particle. Is it correct to say that the particle moves in straight line for t < 0 ? If not, suggest a suitable physical context for this graph.

(A) (A/B) lives closer to the school than (B/A). (B) (A/B) starts from the school earlier than (B/A). (C) (A/B) walks faster than (B/A). (D) A and B reach home at the (same/different) time. (E) (A/B) overtakes (B/A) on the road (once/twice). 3. Give an example of a body possessing zero velocity and still accelerating. 4. What will happen to a hydrogen balloon released on the moon ? 5. Two masses in the ratio 1 : 2 are thrown vertically up with the same speed. What is the effect on the time by the mass ? 6. Why is it not neccessary for a body following another, to stop, to avoid collision ? 7. If in case of a motion, displacement is directly proportional to the square of time elapsed, what do you think about its acceleration i.e., constant or variable ? Explain why ? 8. Why does the earth impart the same acceleration to all bodies ?

(Two Marks Problems) 9. A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x – t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.

Page # 47

12. A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one-tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s. 13. Explain clearly, with examples, the distinction between :

(A) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval ; (B) magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both ( A) and ( B) that the second quantity is either greater than or equal to the first. When is the equality sign true ? [For the sake of convenience, consider one-dimensional motion only]. 14. Two parallel rail tracks run north-south. Train A moves due north with a speed of 54 km h –1 and train B moves due south with a speed of 90 km h –1. What is the relative velocity of B with respect to A in m s –1? 15. Deduce the following relation v2 – u2 = 2as where symbols have their usual meaning. 16. If the length and time period of an oscil lating pendulum have errors of 1% and 2% respectively, what is the error in the estimate of g ?


Master Your Physics - NEET / AIIMS 17. Two straight lines drawn on the same displacement – time graph make angles 30 o and 60o with time axis respectively in the figure. Which line represents greater velocity ? What is the ratio of the velocity of line A to the velocity of line B ?

18. The driver of a truck travelling with a velocity v suddenly notices a brick wall in front of him at a distance d . Is it better for him to apply brakes or to make a circular turn without appling brakes in order to just avoid crashing into the wall ? Why ?

(Three Marks Problems)

KINEMATICS -1

each interval.

22. State with reasons which of these following graphs cannot possible represent one-dimensional motion of a particle.

(A)

(B)

19. In which of the following examples of motion, can the body be considered approximately a point object:

(A) a railway carriage moving without jerks between two stations. (B) a monkey sitting on top of a man, cycling smoothly on a circular track.

(C)

(D)

(C) a spinning cricket ball that turns sharply on hitting the ground.

23. The distance x travelled by a body in a straight line is directly proportional to t 2. Decide on the

(D) a tumbling beaker that has slipped off the edge of a table.

type of motion associated. If x  t 3 what change will you observe ?

20. Figure gives the x – t plot of a particle executing one-dimensional simple harmonic motion. Give the signs of position, velocity and acceleration variables of the particle at t = 0.3 s, 1.2 s, –1.2 s.

24. A police van moving on a highway with a speed of 30 km/h fires a bullet at a thief ’s car speeding away in the same direction with a speed of 192 km/h. If the muzzle speed of the bull et is 150 ms –1, with what speed does the bullet hit the thief’s car ? 25. On a two lane road, car A is travelling with a speed of 36 kmh –1. Two cars B and C approach car A in opposite directions with a speed of 54 kmh –1 each. At a certain instant, when distance AB is equal to AC, both being 1 km, B decides to overtake A before C does. What minimum acceleration of car B is required to avoid an accident ?

21. Figure gives the x – t plot of a particle in onedimensional motion. Three different equal intervals of time are shown. In which interval is the average speed the greatest and in which is it the least? Give the sign of average velocity for

Page # 48

26. A car moving along a straight highway with speed of 126 km h –1 is brought to a stop within a distance of 200 m. What is the retardation of the car (assumed uniform) and how long does it take for the car to stop?


Master Your Physics - NEET / AIIMS 27. A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km/ hr. Finding the market closed, he instantly turns, and walks back home with a speed of 7.5 km/ hr. What is the (a) magnitude of average velocity, and (b) average speed of the man over the interval of time (i) 0–30 minutes (ii) 0–50 minutes (iii) 0–40 minutes ?

( Five Marks Questions) 28. Derive the three equations of motion by calculus method. Express conditions under which they can be used. 29. (A) With the help of a simple case of an object moving with constant velocity show that the area under velocity-time curve represents the dis-

KINEMATICS -1

placement over a given time inteval. (B) Establish the relation x  v0t 

1 2

at 2

graphically. (C) A car moving with a speed of 126 km/h is brought to a stop within a distance of 200 m. Calculate the retardation of the car and the time required to stop it. 30. Draw velocity–time graph of uniformly accelerated motion in one dimension. From the velocity time graph of uniform accelerated motion deduce the equations of motion in distance

and time.

Mock Test-2 Time : 3 hrs.

M. M. : 70

(One Mark Problems) 1. What will be the nature of velocity–time graph for a uniform motion ?

11. Do the following two graphs represent same type of motion ? Name the motion.

2. The position coordinates of a moving particle is given by x = 6 + 18t + 9t 2 ( x in metres and t in seconds). What is its velocity at t = 2 sec.? 3. A lorry and a car with the same kinetic energy are brought to rest by the application of brakes which provide equal retarding forces. Which of them will come to rest in a shorter distance ? 4. Write two uses of v-t graph ? 5. What is the ratio of SI to CGS unit of acceleration ? 6. What does speedometer of a car indicate ? 7. When a body accelerates by  t , what is the velocity after time ‘t’, when it starts from rest? 8. What is the ratio of the time taken to go up and come down by a body thrown vertically up? (Two marks problems ) 9. Two balls have the same size, but one is denser than the other. Assume that the air resistance is same in each case. Show that when they are released simultaneously from the same height, the heavier ball will reach the ground first. 10. Two bodies of different masses ml and m2 are dropped from two different heights ‘a’ and ‘b’. What is the ratio of time taken by the two to drop through these distances ?

Page # 49

12. A body starts from rest and moves along a straight line. It has uniformly accelerated motion upto time t 1 During the interval t 2 - t 1 it moves with uniform velocity. After time t 2 its motion is retarded, and it comes to rest at t ime t 3. Draw the velocity-time graph. 13. Which of the two : Velocity or acceleration gives the direction motion of a body ? Justi fy your answer by an example. 14. A ball is thrown vertically up with a velocity of 20 m/s. Construct time-acceleration and time-displacement graph. 15. Two balls of different masses are thrown vertically upwards with same initial speed. Which one will rise to the greater height ? Which of the two will come back with greater speed to the point of projection ? 16. Derive the relation, v2 = u2 + 2as where the symbols carry usual meaning. 17. A body dropped from a moving frame of reference, will have the velocity of the frame. Ex plain.


Master Your Physics - NEET / AIIMS 18. Velocity-time graph of a moving object is shown below. What is the acceleration of the object ? Also draw displacement-time graph for the motion of the object.

KINEMATICS -1

(D) To what height does the ball rise and after how long does the ball return to the player’s hands? (Take g = 9.8 m s –2 and neglect air resistance). 24. Read each statement below carefully and state with reasons and examples, if it is true or false :

A particle in one-dimensional motion (A) with zero speed at an instant may have nonzero acceleration at that instant (Three Marks Problems) 19. Two cars A and B are running at velocities of 60 km/hr and 45 km/hr respectively. Calculate the relative velocity of car A if: (i) they are both travelling eastwards and (it) car A is travelling eastwards and car B is travelling westwards. 20. A particle starts from rest, and its acceleration (a) plotted against time (t) is shown below. Plot the corresponding velocity (v) against time (t). Also plot the corresponding displacement (s) against time (t ).

21. A motorboat covers the distance between two ports on the river in t 1 = 8 hr and t 2 = 12 hr downstream and upstream respectively. What is the time required for the boat to cover this distance in still water ? 22. A body starts accelerating uniformly a from a velocity ‘u’ and travels in a straight line. Prove

that it covers a length of u 

a 2

(2t  1) in the t th

second of motion.

(B) with zero speed may have non-zero velocity, (C) with constant speed must have zero acceleration, (D) with positive value of acceleration must be speeding up. 25. Suggest a suitable physical situation for each of the following graphs :

26. A three-wheeler starts from rest, accelerates uniformly with 1 m s –1 on a straight road for 10 s, and then moves with uniform velocity. Plot the distance covered by the vehicle during the nth second (n = 1, 2, 3, ....) versus n. What do you expect this plot to be during accelerated motion : a straight line or a parabola ? 27. Two stones are thrown up simultaneously from the edge of a cliff 200 m high with initial speeds of 15 m s –1 and 30 m s –1. Verify whether the graph shown, correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take g = 10 m s –2. Give the equations for the linear and curved parts of the plot.

23. A player throws a ball upwards with an initi al speed of 29.4 ms –1.

(A) What is the direction of acceleration during the upward motion of the ball ? (B) What are the velocity and acceleration of the ball at the highest point of its motion ? (C) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of x-axis, and give the signs of position, velocity and acceleration of the ball during its upward, and downward motion.

Page # 50



KINEMATICS -1

(Three Long Problems) 28. A point object is thrown vertically upwards at such a speed that it returns to the thrower after 6 seconds. With what speed was it thrown up and how high did it rise? Plot speed time graph for the object and use it to find the distance travelled by it in the last second of its journey. 29. Derive an equation for the distance covered by a uniformly accelerated body in nth second of its motion. A body travels half its total path in the last second of its fall from rest. 30. On a long horizontal moving belt, a child runs

to and for with a speed 9 km h –1 (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h –1. For an observer on a stationary platform outside, what is the (A) speed of the child running in the direction of motion of the belt ? (B) speed of the child running opposite to the direction of motion of the belt ? (C) time taken by the child in (a) and (b) ? Which of the answers alter if motion is viewed by one of the parents ?

Page # 51



KINEMATICS -1

Objective Questions 1.

An athlete completes one round of a circular track of radius R in 40 sec. What will be his displacement at the end of 2 min. 20 sec. (A) Zero (B) 2R (C) 2R

2.

(B) A body having zero velocity will necessarily have zero acceleration. (C) A body having uniform speed can have only uniform acceleration.

(D) 7R

(D) A body having non–uniform velocity will have zero acceleration.

A person travels along a straight road for half the distance with velocity 1 and the remaining half distance with velocity 2. The aver-

8.

age velocity is given by : (A)

(C) 3.

12

(B)

1  2 2

6.

2 1 2

1   2

3

(B) 1 :

3 : 1

(C)

5.

(A) S1 = S2 (C) S1 = S2 / 2

The displacement–time graph for two particles A and B are straight lines inclined at angles of 30º and 60º with the time axis. The ratio of velocities of VA : V B is : (A) 1 : 2

4.

(D)

22 12

(D) 1 : 3

A car moves for half of its time at 80 km/h and for rest half of time at 40 km/h. Total distance covered is 60 km. What is the average speed of the car : (A) 60 km / h (B) 80 km / h (C) 120 km / h (D) 180 km / h The ratio of the numerical values of the average velocity and average speed of a body is always: (A) Unity (B) Unity or less (C) Unity or more (D) Less than unity th If a car covers 2/5 of the total distance with

1 speed and 3/5th distance with 2 then average speed is : (A)

(C) 7.

1 2

12

2 1 2

1  2

(B)

(D)

1  2 2 51 2 31  2  2

The correct statement from the following is : (A) A body having zero velocity will not necessarily have zero acceleration.

Page # 52

A particle experiences a constant acceleration for 20 sec after starting from rest. If i t travels a distance S1 in the first 10 sec and a distance S2 in the next 10 sec, then :

9.

(B) S1 = S2 / 3 (D) S1 = S2 / 4

An electron starting from rest has a velocity that increases linearly with the time that is  = kt, where k = 2m / sec 2. The distance travelled in the first 3 seconds will be : (A) 9 m (C) 27 m

(B) 16 m (D) 36 m

10. The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is : (A) Increasing with time (B) Decreasing with time (C) Constant but not zero (D) Zero 11. The acceleration of a moving body can be found from : (A) Area under velocity–time graph (B) Area under distance–time graph (C) Slope of the velocity–time graph (D) Slope of distance–time graph 12. The initial velocity of the particle is 10 m/sec and its retardation is 2m/sec2. The distance moved by the particle in 5th second of its motion is : (A) 1 m (C) 50 m

(B) 19 m (D) 75 m

13. The velocity of a body depends on time according to the equation u = 20 + 0.1 t2. The body is undergoing: (A) Uniform acceleration (B) Uniform retardation (C) Non–uniform acceleration (D) Zero acceleration


Master Your Physics - NEET / AIIMS 14. A body starts from rest. What is the ratio of the distance travelled by the body during the 4th and 3rd second : (A) 7/5 (B) 5/7 (C) 7/3 (D) 3/7 15. The acceleration 'a' in m/s2 of a particle is given by a = 3t 2 + 2t + 2 where t is the time. If the particle starts out with a velocity u = 2m /s at t = 0, then th velocity at the end of 2 second is : (A) 12 m/s (B) 18 m/s (C) 27 m/s (D) 36 m/s 16. For a moving body at any instant of time : (A) If the body is not moving, the acceleration is necessarily zero (B) If the body is slowing, the retardation is negative. (C) If the body is slowing, the distance is negative. (D) If displacement, velocity and acceleration at that instant are known, we can find the displacement at any given time in future. 17. Two cars A and B at rest at same point initially. If A starts with uniform velocity of 40 m/sec and B starts in the same direction with constant acceleration of 4m/s2, then B will catch A after how much time : (A) 10 sec (B) 20 sec (C) 30 sec (D) 35 sec 18. A body travels for 15 sec starting from rest with constant acceleration. If it travels distance S1, S 2 and S3 in the first five seconds, second five seconds and next five seconds respectively the relation between S1, S 2 and S3 is : (A) S1 = S2 = S3 (B) 5S1 = 3S2 = S3 (C) S1 =

1 3

S2 =

1 5

S3 (D) S1 =

1 5

S2 =

1 3

S3

19. The position of a particle moving along the x-axis at certain times is given below : t (s) 0 1 2 3 x (m) –2 0 6 16 Which of the following describes the motion correctly : (A) Uniform, accelerated (B) Uniform, decelerated (C) Non–uniform, accelerated (D) There is not enough data for generalization

Page # 53

KINEMATICS -1

20. Consider the acceleration, velocity and dis placement of a tennis ball as it falls to the ground and bounces back. Direction of which of these changes in the process. (A) Velocity only (B) Displacement and velocity (C) Acceleration, velocity and displacement (D) Displacement and acceleration 21. A car moving with a speed of 50 km/hr, can be stopped by brakes after at least 6m. It the same car is moving at a speed of 100 km/hr, the minimum stopping distance is : (A) 6 m (B) 12 m (C) 18 m (D) 24 m 22. A student is standing at a distance of 50 metres from the bus. As soon as the bus begins its motion with an acceleration of 1ms – 2 , the student starts running towards the bus with a uniform velocity u. Assuming the motion to be along a straight road, the minimum value of u, so that the student is able to catch the bus is : (A) 5 ms –1 (B) 8 ms –1 (C) 10 ms –1 (D) 12 ms –1 23. A car starts from rest and moves with uniform acceleration 'a' on a straight road from time t = 0 to t = T. After that, a constant deceleration brings it to rest. In this process the average speed of the car is: (A)

(C)

aT 4 aT 2

(B)

3aT 2

(D) aT

24. An object accelerates from rest to a velocity 27.5 m/s in 10 sec then find distance covered by object in next 10 sec : (A) 550 m (B) 137.5 m (C) 412.5 m (D) 275 m 25. Starting from rest, acceleration of a particle is a = 2(t – 1). The velocity of the particle at t = 5s is: (A) 15 m/sec (B) 25 m/sec (C) 5 m/sec (D) None of these 26. A man is 45 m behind the bus when the bus start accelerating from rest with acceleration 2.5 m/s2. With what minimum velocity should the man start running to catch the bus?



28.

29.

30.

31.

32.

(A) 12 m/s (B) 14 m/s (C) 15 m/s (D) 16 m/s A body A is projected upwards with a velocity of 98 m/s. The second body B is projected upwards with the same initial velocity but after 4 sec. Both the bodies will meet after : (A) 6 sec (B) 8 sec (C) 10 sec (D) 12 sec A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time of : (A) 3 s (B) 5 s (C) 7 s (D) 9 s An iron ball and a wooden ball of the same radius are released from the same height in vacuum. They take the same time to reach the ground. The reason for this is : (A) Acceleration due to gravity in vacuum is same irrespective of the size and mass of the body. (B) Acceleration due to gravity in vacuum depends upon the mass of the body. (C) There is no acceleration due to gravity in vacuum. (D) In vacuum there is a resistance offered to the motion of the body and this resistance depends upon the mass of the body. A stone thrown upward with a speed u from the top of the tower reaches the ground with a velocity 3u. The height of the tower is : (A) 3u2 / g (B) 4u2 / g (C) 6u2 / g (D) 9u2 / g A man in a balloon rising vertically with an acceleration of 4.9 m/sec2 releases a ball 2 sec after the balloon is let go from the ground. The greatest height above the ground reaches by the ball is (g = 9.8 m/sec2) (A) 14.7 m (B) 19.6 m (C) 9.8 m (D) 24.5 m P, Q and R are three balloons ascending with velocities U, 4U and 8U respectively. If stones of the same mass be dropped from each, when they are at the same height, then : (A) They reach the ground at the same time (B) Stone from P reaches the ground first (C) Stone from R reaches the ground first (D) Stone from Q reaches the ground first

Page # 54

KINEMATICS -1

33. With what velocity a ball be projected vertically so that the distance covered by it in 5th second is twice the distance it covers in its 6th second (g = 10 m/s2) (A) 58.8 m/s (B) 49 m/s (C) 65 m/s (D) 19.6 m/s 34. A body thrown vertically upwards with an initial velocity u reaches maximum height in 6 seconds. The ratio of the distance tr avelled by the body in the first second and the seventh second is: (A) 1 : 1 (B) 11 : 1 (C) 1 : 2 (D) 1 : 11 35. A body is thrown vertically upwards with a velocity u. Find the true statement from the following: (A) Both velocity and acceleration are zero at its highest point. (B) Velocity is maximum and acceleration is zero at the highest point. (C) Velocity is maximum and acceleration is g downwards at its highest point. (D) Velocity is zero at the highest point and maximum height reached is u2/2g. 36. A particle when thrown, moves such that it passes from same height at 2 and 10 s, the height is : (A) g (B) 2g (C) 5g (D) 10 g 37. Two balls A and B of same masses are thrown from the top of the building. A, thrown upward with velocity V and B, thrown downward with velocity V, then : (A) Velocity of A is more than B at the ground (B) Velocity of B is more than A at the ground (C) Both A and B strike the ground with same velocity (D) None of these 38. A body falling from a high Minaret travels 40 meters in the last 2 seconds of its fall to ground. Height of Minaret in meters is (g = 10 m/s2) (A) 60 (B) 45 (C) 80 (D) 50 39. A particle starts from rest. Its acceleration (A) versus time (t) is as shown in the figure. The maximum speed of the particle will be :



(A) 110 m/s (B) 55 m/s (C) 550 m/s (D) 660 m/s 40. The variation of velocity of a particle with time moving along a straight line is illustrated in the following figure. The distance travelled by the particle in four seconds is :

(A) 60 m (B) 55 m (C) 25 m (D) 30 m 41. A ball is thrown vertically upwards. Which of the following graph(s) represent velocity–time graph of the ball during its flight (air resistance is neglected)

KINEMATICS -1

(A) Both the particles are having a uniformly accelerated motion. (B) Both the particles are having a uniformly retarded motion. (C) Particle (i) is having a uniformly accelerated motion while particle (ii) is having a uniformly retarded motion. (D) Particle (i) is having a uniformly retarded motion while particle (ii) is having a uniformly accelerated motion. 44. The graph of displacement

Its corresponding velocity–time graph will be :

(A)

(B)

(A)

(B)

(C)

(D)

(C)

(D)

42. The displacement versus time graph for a body moving in a straight line is shown in figure. Which of the following regions represents the motion when no force is acting on the body :

(A) ab (B) bc (C) cd (D) de 43. Figure (i) and (ii) below show the displacement–time graphs of two particles moving along the x–axis. We can say that :

Page # 55

/s time is,

45. Acceleration–time graph of a body is shown. The corresponding velocity–time graph of the same body is :

(A)

(B)

(C)

(D)


Master Your Physics - NEET / AIIMS 46. A particle moves along the sides AB, BC, CD of a square of side 25m with a velocity of 15 ms –1. Its average velocity is :

(A) 15 ms –1 (B) 10 ms –1 (C) 7.5 ms –1 (D) 5 ms –1 47. A car Ais travelling on a straight level road with a uniform speed of 60 km/h. It is followed by another car B which is moving with a speed of 70 km/h. When the distance between them is 2.5 km, the car B is given a deceleration of 20 km/ h2. After how much time will B catch up with A: (A) 1 hr (B) 1/2 hr (C) 1/4 hr (D) 1/8 hr 48. A body moves 6 m north, 8 m east and 10 m verticlly upwards, what is its resultant dis placement from initial position : (A) 10

2m

(B) 10 m

(C) 10/

2m

(D) 10 × 2 m

52. A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total distance covered by the particle during this time is 30 m. Which of the following statements about the motion of the particle is false : (A) Displacement of the particle is zero (B) Average speed of the particle is 3 m/s (C) Displacement of the particle is 30 m (D) Both (A) and (B) 53. A particle moves along a semicircle of radius 10m in 5 seconds. The average velocity of the particle is: (A) 2 ms –1 54.

55.

49. A person moves 30 m north and then 20 m towards east and finally 30

2 m in south-

west direction. The displacement of the person from the origin will be : (A) 10 m along north (B) 10 m along south (C) 10 m along west (D) Zero 50. A wheel of radius 1 metre rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of the wheel initially in contact with the ground is : (A) 2 (C)

2  4

(D)

57.

58.



51. A car travels from A to B at a speed of 20 km/hr and returns at a speed of 30 km/hr. The average speed of the car for whole journey is : (A) 25 km/hr (B) 24 km/hr (C) 50 km/hr (D) 5 km/hr

Page # 56

56.

2 

(B)

KINEMATICS -1

59.

(B) 4 ms –1

(C) 2 ms –1 (D) 4 ms –1 The instantaneous velocity of a body can be measured : (A) Graphically (B) Vectorially (C) By speedometer (D) None of these A body under the action of several forces will have zero acceleration : (A) When the body is very light (B) When the body is very heavy (C) When the body is a point body (D) When the vector sum of all the forces acting on it is zero A motor car moving with a uniform speed of 20 m/sec comes to stop on the application of brakes after travelling a distance of 10 m. Its acceleration is : (A) 20 m / sec2 (B) –20 m / sec 2 (C) –40 m / sec2 (D) + 2m / sec2 The velocity of a body moving with a uniform acceleration of 2m / sec 2 is 10 m/sec. Its velocity after an interval of 4 sec is : (A) 12 m / sec (B) 14 m / sec (C) 16 m / sec (D) 18 m / sec A particle moving with a uniform acceleration travels 24 m and 64 m in the first two consecutive intervals of 4 sec each. Its initial velocity is : (A) 1 m/sec (B) 10 m/sec (C) 5 m/sec (D) 2 m/sec An alpha particle enters a hollow tube of 4 m length with an initial speed of 1 km/s. It is accelerated in the tube and comes out it with a speed of 9 km/s. The time for which it remains inside the tube is:


Master Your Physics - NEET / AIIMS (A) 8 × 10 –3 s (B) 80 × 10 –3 s (C) 800 × 10 –3 s (D) 8 × 10 –4 s 60. Two cars A and B are travelling in the same direction with velocities 1 and 2 (1 > 2). When the car A is at a distance d ahead of the car B, the driver of the car A applied the brake producing a uniform retardation a. There will be no collision when : (A) d < (C) d >

( 1   2 ) 2 2a ( 1   2 ) 2a

(B) d <

2

(D) d >

12   2 2 2a 2 1

  2 2 2a

61. A body of mass 10 kg is moving with a constant velocity of 10 m/s. When a constant force acts for 4 seconds on it, it moves with a velocity 2 m/sec in the opposite direction. The acceleration produced in it is : (A) 3 m/sec2 (B) –3 m/sec2 (C) 0.3 m/sec2 (D) –0.3 m/sec2 62. A car moving with a velocity of 10 m/s can be stopped by the application of a constant force F in a distance of 20 m. If the velocity of the car is 30 m/s, it can be stopped by this force in : (A)

20 3

m

(B) 20 m

(C) 60 m (D) 180 m 63. A boggy of uniformly moving train is suddenly detached from train and stops after convering some distance. The distance covered by the boggy and distance covered by the train in the same time has relation : (A) Both will be equal (B) First will be half of second (C) First will be 1/4 of second (D) No definite ratio 64. A particle moves along a straight line such that its displacement at any time t is given by S = t3 – 6t2 + 3t + 4 metres. The velocity when the acceleration is zero is : (A) 3 ms –1 (B) –12 ms –1 (C) 42 ms –1 (D) –9 ms –1 65. If a train travelling at 72 kmph is to be brought to rest in a distance of 200 metres, then its retardation should be : (A) 20 ms –2 (B) 10 ms –2 (C) 2 ms –2 (D) 1 ms –2

Page # 57

KINEMATICS -1

66. The displacement of a particle starting from rest (at t = 0) is given by s = 6t2 – t3. The time in seconds at which the particle will attain zero velocity again, is : (A) 2 (B) 4 (C) 6 (D) 8 67. A particle travels 10m in first 5 sec and 10m in next 3 sec. Assuming constant acceleration what is the distance travelled in next 2 sec. (A) 8.3 m (B) 9.3 m (C) 10.3 m (D) None of above 68. The motion of a particle is described by the equation u = at. The distance travelled by the particle in the first 4 seconds : (A) 4a (B) 12a (C) 6a (D) 8a 69. A body of 5 kg is moving with a velocity of 20 m/s. If a force of 100N is applied on it for 10s in the same direction as its velocity, what will now be the velocity of the body : (A) 200 m/s (B) 220 m/s (C) 240 m/s (D) 260 m/s 70. The engine of a motorcycle can produce a maximum acceleration 5 m/s 2. Its brakes can produce a maximum retardation 10 m/s2. What is the minimum time in which it can cover a distance of 1.5 km: (A) 30 sec (B) 15 sec (C) 10 sec (D) 5 sec 71. A body A moves with a uniform acceleration a and zero initial velocity. Another body B, starts from the same point moves in the same direction with a constant velocity . The two bodies meet after a time t. The value of t is : (A) 2/a

(B)

/2a

(D)

(C)

/a

 2a

72. The displacement of a particle is proportional to the cube of time elapsed. How does the acceleration of the particle depends on time obtained : (A) a (C) a

 

 2t a  t

t2

(B) a

t3

(D)


Master Your Physics - NEET / AIIMS 73. A body is moving with uniform acceleration describes 40 m in the first 5 sec and 65 m in next 5 sec. Its initial velocity will be : (A) 4 m/s (B) 2.5 m/s (C) 5.5 m/s (D) 11 m/s 74. Speed of two identical cars are u and 4u at a specific instant. The ratio of the respective distances in which the two cars are stopped from that instant is : (A) 1 : 1 (B) 1 : 4 (C) 1 : 8 (D) 1 : 16 75. A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S, then : (A) S = (C) S =

1

ft 2

2 1

72

ft

(B) S = 2

(D) S =

1 4 1 6

ft 2 ft

2

76. A particle moves along x–axis as x = 4(t – 2) + a(t – 2)2. Which of the following is true? (A) The initial velocity of particle is 4. (B) The acceleration of particle is 2a. (C) The particle is at origin at t = 0. (D) None of these 77. A body starting from rest moves with constant acceleration. The ratio of distance covered by the body during the 5th sec to that covered in 5 sec is : (A) 9/25 (C) 25/9

(B) 3/5 (D) 1/25

(A) 5 m/sec; 1 m/sec (B) 4 m/sec ; 1 m/sec

Page # 58

(C)

a :

b

(D) a2 : b2

81. A stone is dropped into water from a bridge 44.1 m above the water. Another stone is thrown vertically downward 1 sec later. Both strike the water simultaneously. What was the initial speed of the second stone: (A) 12.25 m/s (C) 16.23 m/s

(B) 14.75 m/s (D) 17.15 m/s

82. A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is : (A) Equal to the time of fall (B) Less than the time of fall (C) Greater than the time of fall (D) Twice the time of fall 83. A body is released from a great height and falls freely towards the earth. Another body is released from the same height exactly one second later. The separation between the two bodies, two seconds after the release of the second body is : (A) 4.9 m (C) 19.6 m

(B) 9.8 m (D) 24.5 m

84. A body is released from the top of a tower of height h. It takes t sec to reach the ground. Where will be the ball after time t/2 sec : (B) At h/4 from the ground (C) Depends upon mass and volume of the body (D) At 3h/4 from the ground 85. Two stones of different masses are dropped simultaneously from the top of a building (A) Smaller stone hit the ground earlier

(D) 5 m/

(B) Larger stone hit the ground earlier (C) Both stone reach the ground simultaneously

79. A stone falls from a balloon that is descending at a uniform rate of 12 m/s. The displacement of the stone from the point of release after 10 sec is : (A) 490 m (C) 610 m

80. Two bodies of different masses ma and m b are dropped from two different heights a and b. The ratio of the time taken by the two to cover these distance are : (A) a : b (B) b : a

(A) At h/2 from the ground

78. The distance between two particles is decreasing at the rate of 6m/sec. If these particles travel with same speeds and in the same direction, then the separation increase at the rate of 4m/sec. The particles have speeds as :

(C) 4 m/sec ; 2 m/sec sec ; 2 m/sec

KINEMATICS -1

(B) 510 m (D) 725 m

(D) Which of the stones reach the ground earlier depends on the composition of the stone 86. A body thrown with an initial speed of 96 ft/ sec reaches the ground after (g = 32 ft/sec) (A) 3 sec (C) 12 sec

(B) 6 sec (D) 8 sec


Master Your Physics - NEET / AIIMS 87. A stone is dropped from a certain height which can reach the ground in 5 second. If the stone is stopped after 3 second of its fall and then allowed to fall again, then the time taken by the stone to reach the ground for the remaining distance is :

88.

89.

90.

91.

92.

93.

94.

(A) 2 sec (B) 3 sec (C) 4 sec (D) None of these A particle is dropped under gravity from rest from a height h (g = 9.8 m/s2) and it travels a distance 9h/25 in the last second, the height h is : (A) 100 m (B) 122.5 m (C) 145 m (D) 167.5 m A balloon is at a height of 81 m and is ascending upwards with a velocity of 12 m/s. A body of 2 kg weight is dropped from it. If g = 10 m/s2, the body will reach the surface of the earth in : (A) 1.5 s (B) 4.025 s (C) 5.4 s (D) 6.75 s A ball is thrown vertically upwards from the top of a tower at 4.9 ms –1. It strikes the pond near the base of the tower after 3 seconds. The height of the tower is : (A) 73.5 m (B) 44.1 m (C) 29.4 m (D) None of these A bullet is fired wtih a speed of 1000 m/sec in order to hit a target 100 m away. If g = 10 m/s2, the gun should be aimed : (A) Directly towards the target (B) 5 cm above the target (C) 10 cm above the target (D) 15 cm above the target A body starts to fall freely under gravity. The distance covered by it in first, second and third second are in ratio : (A) 1 : 3 : 5 (B) 1 : 2 : 3 (C) 1 : 4 : 9 (D) 1 : 5 : 6 A stone is shot straight upward with a speed of 20 m/sec from a tower 200 m high. The speed with which it strikes the ground is approximately : (A) 60 m/sec (B) 65 m/sec (C) 70 m/sec (D) 75 m/sec A body projected vertically upwards with a velocity u returns to the starting point in 4 seconds. If g = 10 m/sec 2, the value of u is :

Page # 59

KINEMATICS -1

(A) 5 m/sec (B) 10 m/sec (C) 15 m/sec (D) 20 m/sec 95. A body is thrown vertically up from the ground. It reaches a maximum height of 100m in 5 sec. After what time it will reach the ground from the maximum height position : (A) 1.2 sec (B) 5 sec (C) 10 sec (D) 25 sec 96. A body thrown upwards with some velocity, reaches the maximum height of 20 m. Another body with double the mass thrown up, with double initial velocity will reach a maximum height of : (A) 200 m (B) 16 m (C) 80 m (D) 40 m 97. A balloon starts rising from the ground with an acceleration of 1.25 m/s2 after 8s, a stone is released from the balloon. The stone will (g = 10 m/s2) (A) Reach the ground is 4 second (B) Begin to move down after being released (C) Have a displacement of 50 m ( D ) Cover a distance of 40 m in reaching the ground 98. A man throws a ball vertically upward and it rises through 20 m and returns to his hands. What was the initial velocity (u) to the ball and for how much time (T) it remained in the air (g = 10 m/s2) (A) u = 10 m/s, T = 2s (B) u = 10 m/s, T = 4s (C) u = 20 m/s, T = 2s (D) u = 20 m/s, T = 4s 99. A ball is dropped from top of a tower of 100 m height. Simultaneously another ball was thrown upward from bottom of the tower with a speed of 50 m/s (g = 10 m/s 2). They will cross each other after: (A) 1 s (B) 2 s (C) 3 s (D) 4 s 100. A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is 5m, the number of ball thrown per minute is (g = 10 m/s2) (A) 120 (B) 80 (C) 60 (D) 40


Master Your Physics - NEET / AIIMS 101. A ball is released from the top of a tower of height h meters. It takes T seconds to reach the ground. What is the position of the ball in T/3 seconds : (A) h/9 meters from the ground (B) 7h/9 meters from the ground (C) 8h/9 meters from the ground (D) 17h/18 meters from the ground 102. Two balls of same size but the density of one is greater than that of the other are dropped from the same height, then which ball will reach the earth first (air resistance is negligible) : (A) Heavy ball (B) Light ball (C) Both simultaneously (D) Will depend upon the density of the balls 103. A packet is dropped from a balloon which is going upwards with the velocity 12 m/s, the veocity of the packet after 2 seconds will be : (A) –12 m/s (B) 12 m/s (C) –7.6 m/s (D) 7.6 m/s 104. If a freely falling body travels in the last second a distance equal to the distance travelled by it in the first three second, the time of the travel is : (A) 6 sec (B) 5 sec (C) 4 sec (D) 3 sec 105. From the top of a tower two stones, whose masses are in the ratio 1 : 2 are thrown one straight up with an initial speed u and the second straight down with the same speed u. Then, neglecting air resistance: (A) The heavier stone hits the ground with a higher speed (B) The lighter stone hits the ground with a higher speed (C) Both the stones will have the same speed when they hit the ground. (D) The speed can't be determined with the given data. 106. An object start sliding on a frictionless inclined plane and from same height another object start falling freely : (A) Both will reach with same speed (B) Both will reach with same acceleration (C) Both will reach in same time (D) None of above

Page # 60

KINEMATICS -1

107. A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is : (A) 4.0 m/s (B) 5.0 m/s (C) 5.5 m/s (D) 4.8 m/s 108. A small block slides without friction down an inclined plane starting from rest. Let Sn be the distance travelled from time t = n – 1 to t = n. Then

(A)

(C)

Sn Sn 1

2n  1 2n 2n  1 2n  1

is :

(B)

(D)

2n  1 2n  1 2n 2n  1

109. The  – t graph of a moving object is given in figure. The maximum acceleration is

(A) 1cm/sec2 (B) 2cm/sec2 (C) 3cm/sec2 (D) 6cm/sec2 110. The x–t graph shown in figure represents (A) Constant velocity (B) Velocity of the body is continuously changing (C) Instantaneous velocity (D) The body travels with constant speed upto time t1 and then stops 111. A lift is going up. The variation in the speed of the lift is as given in the graph. What is the height to which the lift takes the passengers :


Master Your Physics - NEET / AIIMS (A) 3.6 m (B) 28.8 m (C) 36.0 m (D) Cannot be calculated from the above graph 112. The velocity–time graph of a body moving in a straight line is shown in the figure. The displacement and distance travelled by the body in 6 sec are respectively :

(A) 8 m, 16 m (B) 16 m, 8 m (C) 16 m, 16 m (D) 8 m, 8 m 113. For the velocity–time graph shown in figure below the distance covered by the body in last two seconds of its motion is what fraction of the total distance covered by it in all the seven seconds.

KINEMATICS -1

(A)

(B)

(C)

(D)

116. The area under acceleration–time graph gives : (A) Distance travelled (B) Change in acceleration (C) Force acting (D) Change in velocity 117. Which graph represents the uniform acceleration :

(A)

(B)

(C)

(D)

118. Which of the following velocity–time graphs represent uniform motion :

(A)

(C)

1 2 1 3

(B)

(D)

1

(B)

(C)

(D)

4 2 3

114. The displacement–time graph of moving particle is shown below,

The instantaneous velocity of the particle is negative at the point : (A) D (B) F (C) C (D) E 115. Which of the following graph represents uniform motion :

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(A)

119. From the following displacement–time graph find out the velocity of a moving body :

(A)

(C)

1 3

m/s

3 m/s

(B) 3 m/s

(D)

1 3

m/s


Master Your Physics - NEET / AIIMS 120. The

 – t plot of a moving object is shown

in the figure. The average velocity of the object during the first 10 seconds is :

(A) 0 (B) 2.5 ms –1 (C) 5 ms –1 (D) 2 ms –1 121. A car travels a distance S on a straight road in two hours and then returns to the starting point in the next three hours. Its average velocity is : (A) S / 5 (B) 2S / 5 (C) S / 2 + S / 3 (D) None of the above 122. A body has speed V, 2V and 3V in first 1/3 of distance S, seconds 1/3 of S and third 1/ 3 of S respectively. Its average speed will be : (A) V (B) 2V (C) 18/11 V (D) 11/18 V 123. If the body covers one–third distance at speed

1, next one third at speed 2 and last one third at speed 3, then average speed will be : (A) (B) (C) (D)

12  2 3  31 1  2  3 1  2  3 3

1 2  3 1 2   2  3   31 31 2  3

12  2 3  31

124. If the velocity of a particle is (10 + 2t2)m/s, then the average acceleration of the particle between 2s and 5s is : (A) 2 m/s2 (B) 4 m/s2 (C) 12 m/s2 (D) 14 m/s2 125. A thief is running away on a straight road in jeep moving with a speed of 9 ms –1. A police man chases him on a motor cycle moving at a speed of 10 ms –1. If the instantaneous separation of the jeep from the motorcycle is 100 m, how long will it take for the police to catch the thief: (A) 1 s (B) 19 s (C) 90 s (D) 100 s 126. The speed of a body moving with uniform acceleration is u. This speed is doubled while

Page # 62

KINEMATICS -1

covering a distance S. When it covers an additional distance S, its speed would become : (A)

3u

(B)

5u

(C)

11 u

(D)

7u

127. Two trains one of length 100 m and another of length 125 m, are moving in mutually opposite directions along parallel lines, meet each other, each with speed 10 m/s. If their acceleration are 0.3 m/s2 and 0.2 m/s2 respectively, then the time they take to pass each other will be : (A) 5 s (B) 10 s (C) 15 s (D) 20 s 128. A body starts from rest with uniform acceleration. If its velocity after n second is , then its displacement in the last two seconds is : (A) (C)

2 ( n  1) n

( n  1) n

(B) (D)

( n  1) n 2 ( n  1) n

129. A particle is moving in a straight line and pass through a point O with a velocity of 6 ms –1. The particle moves with a constant retardation of 2 ms –2 for 4 s and there after moves with constant velocity. How long after leaving O does the particle return to O : (A) 3 s (B) 8 s (C) Never (D) 4 s 130. A bird flies for 4 s with a velocity of |t – 2| m/s in a straight line, where t is time in secnods. It covers a distance of : (A) 2 m (B) 4 m (C) 6 m (D) 8 m 131. A body is projected vertically up with a velocity

 and after some time it returns to the point from which it was projected. The average velocity and average speed of the body for the total time of flight are : (A)



 /2 and /2

(C) 0 and 0

(B) 0 and (D)

/2



 /2 and 0

132. A stone is dropped from a height h. Simultaneously, another stone is thrown up from the ground which reaches a height 4 h. The two stones cross each other after time :

(A)

(C)

h 8g

2gh

(B)

(D)

8gh h 2g



KINEMATICS -1

133. Four marbles are dropped from the top of a tower one after the other with an interval of one second. The first one reaches the ground after 4 seconds. When the first one reaches the ground the distances between the first and second, the second and third and the third and forth will be respectively : (A) 35, 25 and 15 m (B) 30, 20 and 10 m (C) 20, 10 and 5 m (D) 40, 30 and 20 m 134. A balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is :

h

(A) 4

(C)

h

(B) 2

g 2h

g

(D)

g

g

h

135. Two bodies are thrown simultaneously from a tower with same initial velocity

0 :

one

vertically upwards, the other vertically downwards. The distance between the two bodies after time t is: (A) 20t +

(C)

0t

+

1 2 1 2

gt2

gt2

(B) 20t

0t

(D)

136. A particle is projected upwards. The times corresponding to height h while ascending and while descending are t1 and t2 respectively. The velocity of projection will be : (A) gt1 (B) gt2 (C) g(t1 + t2)

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((D)

g( t 1  t 2 ) 2



If a body A of mass M is thrown with velocity V at an angle of 30º to the horizontal and another body B of the same mass is thrown with the same speed at an angle of 60º to the horizontal. The ratio of horizontal range of A [CBSE PMT 1992] to B will be : (A) 1 : 3 (C) 1 :

2.

6.

(B) 1 : 1 (D)

3

3 :1

A ball P is dropped vertically and another ball Q is thrown horizontally with the same velocities from the same height and at the same time. If air resistance is neglected, then

KINEMATICS -1

Two trains travelling on the same track are approaching each other with equal speeds of 40 m/s. The drivers of the trains begin to decelerate simultaneously when they are just 2.0 km apart. Assuming the decelerations to be uniform and equal, the value of the deceleration to barely avoid collision should be: [AMU 1995] (A) 11.8 m/s2 (C) 2.1 m/s2

7.

(B) 11.0 m/s2 (D) 0.8 m/s2

Two trains, each 50 m long are travelling in opposite direction with velocity 10 m/s an 15 m/s. The time of crossing is :

[BHU 1994]

[CPMT 1995]

(A) Ball P reaches the ground first

(A) 2s

(B) Ball Q reaches the ground first

(C) 2

(C) Both reach the ground at the same time

8.

(D) The respective masses of the two balls will decide the time 3.

A car accelerates from rest at a constant rate 

time elapsed is t, then the maximum velocity [CPMT 1994] acquired by the car is: (A)

(C) 4.

F  2  2 I t GH  J K (   ) t



(D)

t 

A boy walks to his school at a distance of 6 km with constant speed of 2.5 km/hr and walks back with a constant speed of 4 km/hr. His average speed for round trip expressed in km/ [AFMC 1995] hr is: (A) 24/13 (C) 3

5.

(B)

F  2   2 I t GH  J K

(B) 40/13 (D) 1/2

The initial velocity of a particle is u (at t = 0) and the acceleration f is given by at. Which of the following relation is valid : [BHU 1995]

(A) (C)

 = u +  = u +

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at at

2

 = u + (D)  = u

(B)

a

t2 2

3s

(D) 4

9.

3s

An object is projected upwards with a velocity of 100 m/s. It will strike the ground after [AFMC 1995] (approximately) (A) 10 sec (C) 15 sec

for some time, after which it deceleates at a constant rate  and comes to rest. If the total

(B) 4s

(B) 20 sec (D) 5 sec

Water drops fall at regular intervals from a tap which is 5 m above the ground. The third drop is leaving the tap at the instant the first drop touches the ground. How far above the ground is the second drop at that instant : [CPMT 1995]

(A) 2.50 m (C) 4.00 m

(B) 3.75 m (D) 1.25 m

10. The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity 0. The distance travelled by the particle in time t will [CPMT 1995] be: (A)

0t

+

(C)

0t

+

1

bt2

(B)

0t

+

bt3

(D)

0t

+

3 1 6

1

bt3

3 1 2

bt2

11. A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement time graph is characterised by : [AIIMS 1995]


Master Your Physics - NEET / AIIMS (A) Negative slope and zero curvature (B) Zero slope and negative curvature (C) Zero slope and positive curvature (D) Positive slope and zero curvature 12. A car travels the first half of a distance between two places at a speed of 30 km/hr and the second half of the distance at 50 km/hr. The average speed of the car for the whole [AFMC 1996] journey is : (A) 42.5 km/hr (C) 37.5 km/hr

(B) 40.0 km/hr (D) 35.0 km/hr

13. A 120 m long train is moving in a direction with speed 20 m/s. A train B moving with 30 m/s in the opposite direction and 130 m long crosses the first train in a time : [CPMT 1996]

(A) 6 s (C) 38 s

(B) 36 s (D) None of these

14. A body dropped from a height h with an initial speed zero, strikes the ground with a velocity 3 km/h. Another body of same mass is dropped from the same height h with an initial speed –u' = 4km/h. Find the final velocity of second body with which it strikes the ground : [CPMT 1996]

(A) 3 km/h (C) 5 km/h

(B) 4 km/h (D) 12 km/h

15. An aeroplane is flying horizontally with a velocity of 600 km/h at a height of 1960 m. When it is vertically at a point A on the ground, a bomb is released from it. The bomb strikes the ground at point B. The distance AB is : [CPMT 1996] (A) 1200 m (C) 3.33 km

(B) 0.33 km (D) 33 km

16. If a body starts from rest and travels 120 cm in the 6th second, then what is the accelera[AFMC 1997] tion: (A) 0.20 m/s2 (C) 0.218 m/s2

(B) 0.027 m/s2 (D) 0.03 m/s2

17. If a car at rest accelerates uniformly to a speed of 144 km/h in 20 s. Then it covers a [CPMT 1997] distance of (A) 20 m (C) 1440 m

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(B) 400 m (D) 2880 m

KINEMATICS -1

18. A truck and a car are moving with equal velocity. On applying the brakes both will stop after certain distance, then : [CPMT 1997] (A) Truck will cover less distance before rest (B) Car will cover less distance before rest (C) Both will cover equal distance (D) None 19. A ball of mass m1 and another ball of mass m2 are dropped from equal height. If time taken by the balls are t1 and t2 respectively, [BHU 1997] then : (A) t1 = t2/2 (C) t1 = 4t2

(B) t1 = t2 (D) t1 = t2/4

20. A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from rest at the top. How much time does it take to cover one–fourth distance starting [CPMT 1997] from rest at the top: (A) 1 s (C) 4 s

(B) 2 s (D) 16 s

21. A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then: [CPMT 1997] (A) t = t1 – t2 (C) t =

t1t 2

(B) t =

t1  t 2 2

(D) t = t12 t22

22. A ball is dropped on the floor from a height of 10 m. It rebounds to a height of 2.5 m. If the ball is in contact with the floor for 0.01 sec, the average acceleration during contact is [CPMT 1997] : (A) 2100 m/sec2 downwards (B) 2100 m/sec2 upwards (C) 1400 m/sec2 (D) 700 m/sec2 23. A stone dropped from the top of the tower touches the ground in 4 sec. The height of the [BHU 1998] tower is about : (A) 80 m (C) 20 m

(B) 40 m (D) 160 m


Master Your Physics - NEET / AIIMS 24. A ball is dropped downwards. After 1 second another ball is dropped downwards from the same point. What is the distance between them [BHU 1998] after 3 seconds : (A) 25 m (C) 50 m

(B) 20 m (D) 9.8 m

25. A train of 150 m length is going towards north direction at a speed of 10 m/sec. A parrot flies at the speed of 5m/sec towards south direction parallel to the railway track. The time taken by the parrot to cross the train is : [BHU 1998]

(A) 12 sec (C) 15 sec

(B) 8 sec (D) 10 sec

26. The displacement x of a particle along a straight line at time t is given by x = a0 + a 1t + a2t2. The acceleration of the particle is : [RPMT 1999]

(A) a0 (B) 2a2

27. The position x of a particle varies with time t as x = at 2 – bt3. The acceleration of the particle will be zero at time t equal to : [BHU 1999]

(B) 2a/3b (D) Zero

28. A stone is thrown with an initial speed of 4.9 m/s from a bridge in vertically upward direction. It falls down in water after 2 sec. The height of the bridge is : [AFMC 1999] (A) 4.9 m (C) 19.8 m

(B) 9.8 m (D) 24.7 m

29. A body freely falling from the rest has a velocity ‘u’ after it falls through a height ‘h’. The distance it has to fall down for its velocity [NHU 1999] to become double, is : (A) 2 h (C) 6 h

(B) 4 h (D) 8 h

30. Speed of a body on reaching the point from which it was projected upwards, is : [AIIMS 1999]

(A) (C)

 = 0  = 0.5

 = 2u (D)  = u

(B) u

31. Time taken by an object falling from rest to cover the height of h1 and h2 is respectively t1 and t2 then the ratio of t 1 to t2 is : [RPMT 1999]

(B)

(C) h1 : 2h2

(D) 2h1 : h2

h2

32. A car moving with a speed of 40 km/h can be stopped by applying brakes after atleast 2m. If the same car is moving with a speed of 80 km/h, what is the minimum stopping [AFMC 2000] distance: (A) 8 m (C) 4 m

(B) 2 m (D) 6 m

33. The motion of a particle is described by the equation x = a + bt2 where a = 15 cm and b = 3 cm/s2. Its instantaneous velocity at time [AMU 2000] 3 sec will be : (B) 18 cm/sec (D) 32 cm/sec

34. A body is moving according to the equation x = at + bt 2 – ct3 where x = displacement and a, b and c are constants. The acceleration of [BHU 2000] the body is : (A) a + 2bt (C) 2b – 6ct

(B) 2b + 6ct (D) 3b – 6ct2

35. The distance travelled by a particle is proportional to the square of time, then the particle [RPMT 2000] travels with: (A) Uniform acceleration (B) Uniform velocity (C) Increasing acceleration (D) Decreasing velocity 36. Acceleration of a particle essentially changes [RPMT 2000] when : (A) Direction of velocity changes (B) Magnitude of velocity changes (C) Both of above (D) Speed changes 37. The relation 3t =

3x + 6 describes the

displacement of a particle in one direction where x is in metres and t in sec. The displacement, when velocity is zero, is : [CPMT 2000] (A) 25 metres (C) 5 metres

Page # 66

h1 :

(A) h1 : h2

(A) 36 cm/sec (C) 16 cm/sec

(B) a1 (D) a2

(A) a/b (C) a/3b

KINEMATICS -1

(B) 12 metres (D) Zero


Master Your Physics - NEET / AIIMS 38. The average velocity of a body moving with uniform acceleration travelling a distance of 3.06 m is 0.34 ms –1. If the change in velocity of the body is 0.18 ms –1 during this time, its uniform acceleration is : [EAMCET 2000] –2

(A) 0.01 ms (C) 0.03 ms –2

39. Equation of displacement for any particle is s = 3t3 + 7t2 + 14t + 8m. Its acceleration at [CPMT 2000] time t = 1 sec is : (A) 10 m/s2 (C) 25 m/s2

(B) 16 m/s2 (D) 32 m/s2

40. A stone is just released from the window of a train moving along a horizontal straight track. The stone will hit the ground following : [BHU 2000]

(A) Straight path (C) Parabolic path

(B) Circular path (D) Hyperbolic path

41. A 150 m long train is moving with a uniform velocity of 45 km / h. The time taken by the train to cross a bridge of length 850 metres [CPMT 2001] is : (A) 56 sec (C) 80 sec

(B) 4 m/s2 (D) 8 m/s2

43. A body A starts from rest with an acceleration a1. After 2 seconds, another body B starts from rest with an acceleration a2. If they travel equal distances in the 5th second, after the start of A, then the ratio a 1 : a2 is equal to [AIIMS 2001] : (A) 5 : 9 (C) 9 : 5

(B) 5 : 7 (D) 9 : 7

44. The velocity of a bullet is reduced from 200 m/s to 100 m/s while travelling through a wooden block of thickness 10cm. The retardation, assuming it to be uniform, will be : [AIIMS 2001]

(A) 10 × 104 m/s2 (B) 12 × 104 m/s2 (C) 13.5 × 104 m/s2 (D) 15 × 104 m/s2

Page # 67

[AFMC 2002]

(A) 40 km/hr (C) 46

2 3

(B) 80 km/hr

km/hr

(D) 36 km/hr

46. A man walks on a straight road from his home to a market 2.5 km away with a speed of 5 km/h. Finding the market closed, he instantly turns and walks back home with a speed of 7.5 km/h. The average speed of the man over the interval of time 0 to 40 min. is equal [AMU 2002] to : (A) 5 km / h (C) 30 / 4 km/h

(B) 25/4 km/h (D) 45 / 8 km/h

47. A person travels along a straight road for the first half time with a velocity 1 and the next half time with a velocity 2. The mean veloc[BHU 2002] ity V of the man is : (A)

2 V



(B) 68 sec (D) 92 sec

42. The displacement of a particle, moving in a straight line, is given by s = 2t2 + 2t + 4 where s is in metres and t in seconds. The accelera[CPMT 2001] tion of the particle is : (A) 2 m/s2 (C) 6 m/s2

45. One car moving on a straight road covers one third of the distance with 20 km/hr and the rest with 60 km/hr. The average speed is :

–2

(B) 0.02 ms (D) 0.04 ms –2

KINEMATICS -1

1



1

1  2

(C) V =

1 2

(B) V =

1  2 2

1 2

(D) V =

48. A particle starts from rest, accelerates at 2 m/ s2 for 10 s and then goes for constant speed for 30s and then decelerates at 4 m/s2 till it stops. What is the distance travelled by it : [AIIMS 2002] (A) 750 m (C) 700 m

(B) 800 m (D) 850 m

49. Three different objects of masses m1, m2 and m3 are allowed to fall from rest and from the same point ‘O’ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio [AIIMS 2002] of : (A) m1 : m2 : m3

(B) m1 : 2m2 : 3m3

(C) 1 : 1 : 1

(D)

1 m1

:

1 m2

:

1 m3

50. From the top of a tower, a particle is thrown vertically downwards with a velocity of 10 m/ s. The ratio of the distances, covered by it in


Master Your Physics - NEET / AIIMS the 3rd and 2nd seconds of the motion is (Take [CPMT 2002] g = 10 m/s2) (A) 5 : 7 (C) 3 : 6

interval of 2 seconds. What should be the speed of the throw so that more than two balls are in the sky at any time (Given g = 9.8 m/ [CPMT 2003] s2) :

(B) 7 : 5 (D) 6 : 3

(A) At least 0.8 m/s (B) Any speed less than 19.6 m/s

51. A particle (A) is dropped from a height and another particle (B) is thrown in horizontal direction with speed of 5 m/sec from the same height. The correct statement is : [CBSE PMT 2002]

(A) Both particles will reach at ground simultaneously

(C) Only with speed 19.6 m/s (D) More than 19.6 m/s 57. If a ball is thrwon vertically upwards with speed u, the distance covered during the last t seconds of its ascent is : [CPMT 2003]

(B) Both particles will reach at ground with same speed (C) Particle (A) will reach at ground first with respect to particle (B). (D) Particle (B) will reach at ground first with respect to particle (A).

(A)

(A) 22.5 m (C) 25.5 m

(B) 25 m (D) 30 m

53. The displacement of a particle is given by y = a + bt + ct2 – dt4. The initial velocity and acceleration are respectively : [CPMT 2003]

(A) b, –4d (C) b, 2c

(B) –b, 2c (D) 2c, –4d

54. Two balls are dropped from heights h and 2h respectively from the earth surface. The ratio of time of these balls to reach the earth is [CPMT 2003]

(A) 1 : (C) 2 : 1

2

(B)

2 :1

(D) 1 : 4

55. The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B : [CPMT 2003]

(A) 18 m (C) 2/3 m

(B) 6 m (D) 2/9 m

56. A man throws balls with the same speed vertically upwards one after the other at an

Page # 68

1 2

gt2

(C) (u – gt)t

(B) ut –

1 2

gt2

(D) ut d

58. An aeroplane flies 400 m north and 300 m west and then flies 1200 m upwards then net [AFMC 2004] displacement is :

52. A man goes 10 m towards North, then 20m towards east then displacement is : [AFMC 2003]

KINEMATICS -1

(A) 1200 m (C) 1400 m 59.

(B) 1300 m (D) 1500 m

The numerical ratio of displacement to the distance covered is always : [BHU 2004] (A) Less than one (B) Equal to one (C) Equal to or less than one (D) Equal to or greater than one

60. A 100 m long train is moving with a uniform velocity of 45 km/hr. The time taken by the train to cross a bridge of length 1 km is : [BHU 2004] (A) 58 s (C) 78 s

(B) 68 s (D) 88 s

61. A police jeep is chasing with, velocity of 45 km/h a thief in another jeep moving with velocity 153 km/h. Police fires a bullet with muzzle velocity of 180 m/s. The velocity it will strike the car of the thief is: [CPMT 2004]

(A) 150 m/s (C) 450 m/s

(B) 27 m/s (D) 250 m/s

62. A particle is thrown vertically upwards. If its velocity at half of the maximum height is 10 m/s, then maximum height attained by it is [CPMT 2004] (Take g = 10 m/s 2) (A) 8 m (C) 12 m

(B) 10 m (D) 16 m


Master Your Physics - NEET / AIIMS 63. A body falls from a height h = 200m (at New Delhi). The ratio of distance travelled in each 2 sec during t = 0 to t = 6 second of the [CPMT 2004] journey is : (A) 1 : 4 : 9 (C) 1 : 3 : 5

(B) 1 : 2 : 4 (D) 1 : 2 : 3

64. A body is thrown vertically upwards with velocity u. The distance travelled by it in the fifth and the sixth seconds are equal. The velocity u is given by (g = 9.8 m/s 2) : [BHU 2004]

(A) 24.5 m/s (C) 73.5 m/s

(B) 49.0 m/s (D) 98.0 m/s

65. A man drops a ball downside from the roof of a tower of height 400 meters. At the same time another ball is thrown upside with a velocity 50 meter/sec from the surface of the tower, then they will meet at which height from the surface of the tower : [CPMT 2003]

(A) 100 meters (C) 80 meters

(B) 320 meters (D) 240 meters

66. Which of the following velocity–time graph shows a realistic situation for a body [AIIMS 2004] in motion :

(A)

(C)

KINEMATICS -1

(D)

68. Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity 1. The boy at A starts running simultaneously with velocity

 and catches

the other boy in a time t, where t is : [CPMT 2005] (A) a/ (C) a /

2  12 ( – 1)

(B)

a 2 / 2  12

(D) a / ( +

1)

69. What determines the nature of the path fol[AFMC 2005] lowed by the particle : (A) Speed (C) Acceleration

(B) Velocity (D) None of these

70. When a ball is thrown up vertically with velocity V0, it reaches a maximum height of 'h'. If one wishes to triple the maximum height then the ball should be thrown with velocity. [AIIMS 2005]

(A) 3V0 (C) 9V0

(B) 3V0 (D) 3/2V0

71. An object is projected at an angle of 45º with the horizontal. The horizontal range and the maximum height reached will be in the ratio.

(B)

[AFMC 2005]

(C)

(A) 1 : 2 (C) 1 : 4

(D)

(B) 2 : 1 (D) 4 : 1

67. An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement(s) – velocity() graph of this object is : [AIIMS 2003]

(A)

Page # 69

(B)


Master Your Physics - NEET / AIIMS 3

KINEMATICS -1

Assertion & Reason

Assertion & Reason Read the assertion and reason carefully to mark the correct option out of the options given below.

5.

(A) If both assertion and reason are true and the reason is the correct explanation of the assertion. (B) If both assertion and reason are true but reason is not the correct explanation of the assertion.

6.

Reason

:

Velocity is a vector quantity and speed is a scalar quantity.

Assertion

:

An object can have constant speed but variable velocity.

Reason

:

Speed is a scalar but velocity is a vector quantity.

Assertion

:

The speed of a body can be negative.

Reason

:

If the body is moving in the opposite direction of positive motion, then its speed is negative.

Assertion

:

The position–time graph of a uniform motion in one dimension of a body can have negative slope.

Reason

:

When the speed of body decreases with time, the position–time graph of the moving body has negative slope.

Assertion

:

A positive acceleration of a body can be associated with a ‘slowing down’ of the body.

Reason

:

Acceleration is a vector quantity.

Assertion

:

A negative accelertion of a body can be associated with a ‘speeding up’ of the body.

Reason

:

Increase in speed of a moving body is independent of its direction of motion.

Assertion

:

When a body is subjected to a uniform acceleration, it always move in a straight line.

Reason

:

Straight line motion is the natural tendency of the body.

Assertion

:

Rocket in flight is not an illustration of projectile.

Reason

:

Rocket takes flight due to combustion of fuel and does

(C) If assertion is true but reason is false. (D) If the assertion and reason both are false.

7.

(e) If assertion is false but reason is true. 1.

2.

Assertion

:

A body is momentarily at rest when it reverses its direction of motion.

Assertion

:

Two balls of different masses are thrown vertically upward with same speed. They will pass through their point of projection in the downward direction with the same speed.

Assertion

Reason

4.

A body can have acceleration even if its velocity is zero at a given instant of time.

Reason

Reason

3.

:

Assertion

Page # 70

:

:

:

:

The maximum height and downward velocity attained at the point of projection are independent of the mass of the ball. If the displacement of the body is zero, the distance covered by it may not be zero.

8.

9.

10.

Displacement is a vector quantity and distance is a scalar quantity. The average velocity of the object over an interval of time is either smaller than or equal to the average speed of the object over the same interval.

11.


Master Your Physics - NEET / AIIMS not move under the gravity effect alone. 12.

Assertion : The average speed of a body

over a given interval of time is equal to the average velocity of the body in the same interval of time if a body moves in a straight line in one direction.

13.

14.

15.

Reason

:

Because in this case distance travelled by a body is equal to the displacement of the body.

Assertion

:

Position–time graph of a stationary object is a straight line parallel to time axis.

Reason

:

For a stationary object, position does not change with time.

Assertion

:

The slope of displacement– time graph of a body moving with high velocity is steeper than the slope of displacement–time graph of a body with low velocity.

Reason

:

Slope of displacement–time graph = Velocity of the body.

Assertion

:

Distance–time graph of the motion of a body having uniformly accelerated motion is a straight line inclined to the time axis.

Reason

16.

Assertion

Reason

17.

Assertion

Page # 71

:

18.

19.

20.

21.

22.

Distance travelled by a body having uniformly accelerated motion is directly proportional to the square of the time taken.

A body having non–zero acceleration can have a constant velocity. : Acceleration is the rate of change of velocity. : A body, whatever its motion is always at rest in a frame of reference which is fixed to the body itself.

KINEMATICS -1

Reason

:

The relative velocity of a body with respect to itself is zero.

Assertion

:

Displacement of a body may be ze ro wh en di st an ce travelled by it is not zero.

Reason

:

The displacement is the longest distance between initial and final position.

Assertion

:

The equation of motion can be applied only if acceleration is along the direction of velocity and is constant.

Reason

:

If the acceleration of a body is constant then its motion is known as uniform motion.

Assertion

:

A bus moving due north takes a turn and starts moving towards east with same speed. There will be no change in the velocity of bus.

Reason

:

Velocity is a vector–quantity.

Assertion

:

The relative velocity between any two bodies moving in opposite direction is equal to sum of the velocities of two bodies.

Reason

:

Sometimes relative velocity between two bodies is equal to difference in velocities of the two.

Assertion

:

The displacement–time graph of a body moving with uniform acceleration is a straight line.

Reason

:

The displacement is pr op or ti on al to ti me fo r uniformly accelerated motion.

Assertion

:

Velocity–time graph for an object in uniform motion along a straight path is a straight line parallel to the time axis.

Reason

:

In uniform motion of an object velocity increases as the square of time elapsed.

:

23.



25.

26.

27.

28.

29.

30.

Assertion

:

A body may be accelerated even when it is moving uniformly.

Reason

:

When direction of motion of the body is changing then body may have acceleration.

Assertion

:

A body falling freely may do so with constant velocity.

Reason

:

The body falls freely, when acceleration of a body is equal to acceleration due to gravity.

Assertion

:

Displacement of a body is vector sum of the area under velocity–time graph.

Reason

:

Displacement is a vector quantity.

Assertion

:

The position–time graph of a body moving uniformly is a straight line parallel to position axis.

Reason

:

The slope of position–time graph in a uniform motion gives the velocity of an object.

Assertion

:

The average speed of an object may be equal to arithmetic mean of individual speed.

Reason

:

Average speed is equal to total distance travelled per total time taken.

Assertion

:

The average and instantaneous velocities have same value in a uniform motion.

Reason

:

In uniform motion, the velocity of an object increases uniformly.

Assertion

:

The speedometer of an automobile measure the average speed of the automobile.

Reason

:

Average velocity is equal to total displacement per total time taken.

Page # 72

KINEMATICS -1



KINEMATICS -1

Answer Key 5.

b and c

6.

(A) 10.4 km (B) 0.62 h.

7.

(A) all tie; (B) 4, tie of 1 and 2, then 3

8.

(A) +40km/h;(B) 40 km/h

9.

(A) 1.74 m/s (B) (2. 135 m/s)

10.

(B)

11.

(B)

12.

(C)

15.

(B)

16.

(C)

17.

(C)

20.

(B)

8.

(a) plus; (b) minus; (c) minus; (d) plus

9.

20 m/s2, in the direction opposite to its init ial velocity

10.

3600 km/ hr, 3600 km/ hr

11.

(A)

1.

150o

2.

6.

(i) y = 5

8.

(a) 

9.

3

10.

135o

,104.5 Crores

12.

y = 0 and x = 0

13. x – 2y + 10 = 0

15.

30o and 150o

16. (C)

3.

()

11.

1 2

6.

7.

(A)

(C) 16.8 km/h

12. (D)

3 2

8.

(A)

(C)

9.

(A)

13.

(B)

14.

(A)

18.

(D)

19.

(C)

(i) x = 3

(ii) x = –2

 17 km./h

13.

(C)

3.

 1

5.

(ii) y = –a

7.

(i) y = –3

(ii) x = 2

(b) 0

(c)



1 6

6

(d)

0

14.

y = mx

1.

()

4.

A straight line parallel to time axis.

5.

A straight line inclined to time axis.

6.

The uniform velocity of the object.

7.

Fig. (a) Infinity (b) Zero. Infact it is not a practical situation.

Page # 73

2.

()

3

17. (A)


Master Your Physics - NEET / AIIMS B

T N E M E C A L P S I D

D A

O 8.

9.

KINEMATICS -1

TIME

Yes, when the velocity of the object is negative

T N E M E C A L P S I D

B D A

O

TIME

10.

vA / vB = tan 30° / tan 45° = (1 /

11.

()

12.

()

13.

(i) infinity (ii) zero

14.

()

15.

()

16.

()

17.

8 m, 16 m

18.

100m, 60m

19.

(i) 170 m, (ii) 125 m, –5 m/s2

20.

A, B, D)

21.

(B)

22.

(D)

23.

(B)

24. (D)

25.

(A, D)

26.

(A)

27.

80 m, 2.5 m/s2

28.

(a) 0.6 m/s2 (b) 50 m

29.

(a) 10 m/s

30.

100 m, zero 31.

x = 5 m, y = 3 m

32.

(B)

33.

(D)

34.

(C)

35.

(B)

36.

(B)

1.

(C)

2.

(A)

3.

(B)

4.

(C)

5.

(C)

6.

(C)

7.

(A)

3.

110 m

4.

0.25 m s –2

5.

136 m

6.

4.5s

7.

2.5 m

8.

2/3 ms –2, 4 ms –2, 65 sec

9.

x = 125 m. 10.

v  2ad

16.

(B)

17.

(B)

18.

(A)

19.

(D)

20.

(C)

21.

(B)

22.

(B)

23.

(A)

24.

(C)

25.

(C)

17.

(C)

18.

(B)

19. (D)

20.

(B)

21.

(A)

22.

(D)

23.

(B)

24. (A)

25.

(A)

26.

(B)

27.

(A)

28.

(B)

29. (D)

30.

(C)

31.

(A)

32.

(A)

Page # 74

3 ) / 1 = 1/ 3

(c) 50m

(b) 20 m/s, zero, 20 m/s, –20 m/s


Kinematics 1r

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