M otion in one dimensions dimensions
EXERCI SE # 1 Q.1.
A runner runner completes completes one round round of a circular circular path of radius radius r in 40 seconds. His His displacement displacement after aft er 2 minutes minutes 20 seconds will be [1] zero
Q.2.
[2] 2 p r
[3] 2r
An old old man goes for morning morning walk on a semicircu semicircular lar track of radius radius 40 m; if he starts from one one end of of the track and and reaches to other end, the distance covered by the man [1] 126 m, 80 m
Q.3.
[ 2] 80 m, 126 m
displacement displacement will respectively be
[3] 80 m, 252 m
[4] 252 m, 80 m
A body body covered a distance distance of L m along along a curved curved path of a quarter quarter circle. The The ratio of distance distance to displacemen displacementt is p
[1] Q.4.
[4] 7p r
[2]
2 2
2 2
2
p
[3]
p
[4]
2
p
A passen passenger ger travels travels alon along g a straigh straightt line line with velocity velocity v 1 for first half time and with velocity v 2 for next half time, then the mean velocity v is given by
[1] v =
Q.5.
v1 + v2 2
[2] v
v2 v1
2 [4] v
[ 2] 60 km/hr
[3] 50 km/hr
1 v2
+
A bicyclist bicyclist enc encoun ounters ters a series series of hill hills. s. Uphi Uphillll speed is always v 1 and downhill speed is always v 2. The total
[1]
v1 v2
A motor otor car car cov cover ers s
rest
[2]
v2 v1
[3]
1 rd part of total distance with v1 3
1 rd part with v 3 3
[1] 18 km/hr Q.8.
1 v1
[4] 48 km/hr
distance travelled is l , with uphill uphill and downhill downhill portions of equal length. length.
Q.7.
=
A car car covers a distance distance of 2 km in 2.5 minu minute, te, if it covers covers half of the distan distance ce with speed 40 km/hr km/hr,, the rest distance distance it will cover with speed [1] 56 km/hr
Q.6.
v1v 2
=
[3] v =
=
=
cyclist's average speed is
v1v2 v1 + v2
[4]
10 km / hr , second
2v1v 2 v1 + v2
1 rd part with v 2 3
=
20 km/hr and
the car? 60 k m / hr . What is the average speed of the [ 2] 45 km/hr
[3] 6 km/hr
[4] 22.5 km/hr
The The displaceme displacement-tim nt-time e graph for the two particles A and B are are straigh st raightt lines lines inclin inclined ed at angles 30 0 and 600 with the time axis. axis. The ratio of t he velocities of A to B will be [1] 1 : 2
Q.9.
[ 2] 1:
3
[3]
[4] 1 : 3
3 :1
The velocity-time graph of a body is shown in figure. figure. The displacement displacement covered covered by the ody in 8 seconds is
[1] 10 m [2] 9 m
) 6 c e / 4 ( 2
5 1
[3] 24 m [4] 30 m
-6
2 3 4
6 7
8
(Sec)
t
M otion in one dimensions dimensions
velocity of a particle moving moving along straight line line is shown shown in figure. figure. The distance traversed by the Q.10. The variation of velocity body in 4 seconds is ) c e s /
[1] 70 m
20
( y t i c10 o l e v
[2] 60 m [3] 40 m
O
1 2 3 Time (sec)
[4] 55 m
4
displacementt y (in metres) of a body varies with t me (in seconds) seconds) according to the equation Q.11. The displacemen
2 y = − t 2 + 16t + 2 . How long does the body come to rest? 3 [1] 8 seconds
[ 2] 10 seconds
[3] 12 seconds
[4] 14 seconds
displacement and t denotes the time and and the displacemen displacementt is given by y = a sin w t , the velocity Q.12. If y denotes the displacement of the particle is
(a cos t w
[1] a c os w t
[2] −a co s w t
[3] a w co s w t
[4]
w
travelling due to North at 20 m/s turns East and travels at the same speed. The change change in its velocity velocity is Q.13. A truck travelling [1] 20 2 m / s No North − East
[2] 20 2 m / s So South − East
[3] 40 2 m / s No North − East
[4] 20 2 m / sN s North − West
t he following equations equations represent the motion motion of a body with finite constant constant acceleration. In these Q.14. Which one of the equations y denotes the displacement of the body at time t and a,b and c are the constant of the motion
[1] y =
a t
+ bt
[ 2] y = at
[3] y = at + bt 2
[4] y = at + bt 2 + ct 3
moving at 12 m/s due east attains a speed 16 m/s m/s towards tow ards north in 4 seconds. The magnitu magnitude de of its average Q.15. A car moving acceleration in m/s 2 is [1] 1 m/s 2
[2] 3 m/s 2
[3] 5 m/s 2
[4] 7 m/s 2
graph shows shows the t he variation of velocity of a rocket with time. Find the time of burnin burning g of fuel from the graph Q.16. Adjacent graph [1] 10 sec [2] 110 sec [3] 120 sec
y / 1 0 0 0 m n i y t i c o l e 10 V
110 x
→ Time (second)
120
[4] cannot be estimated from the graph adjoining g curve represents the velocity-time velocity-time graph of a particle, its it s acceleration values values along OA, AB and BC BC Q.17. The adjoinin in metre/sec 2 are respectively [1] 1,0,–0.5 [2] 1,0,0.5 [3] 1,1,0.5 [4] 1,0.5,0
c e10 – s / n 5 – i y t i c o l e v
A
B
10 20 30 Time in sec
C 40
M otion in one dimensions dimensions
dist ance AB at 30 km/hr next next 1/3 of the distance at 40 km/hr, last 1/3 of the distance Q.18. A car travels first 1/3 of the distance at 24 km/hr. Its average speed in km/hr km/hr for the whole joun jouney ey is [1] 40
[ 2] 35
[3] 30
[4] 28
travels A to M along along a straight straight line line with a veloci velocity ty of 8 m/s and M to A with a velocity velocity of 2 m/s, then the Q.19. A particle travels average velocity for the whole journey journey is [1] 3.2 m/s
[ 2] –5 m/s
[3] –3.2 m/s
[4] 0 m/ s
continue e acceleratin accelerating g untill untill Q.20. An object w ill continu [1] the resultant force on it begins to decrease [2] the velocity changes direction [3] the resultant force on it is zero [4] the resultant force is at right angles to its direction of motion and a graph of her her displaceme displacement nt from home is as shown in figure. figure. Her Her Q.21. A girl w alks along an east-west street, and average velocity for the whole time intervals is distance east (m ) 40 30 A 20 10
[1] zero [2] 6 m/min [3] 11 m/min
B
C
0
5
10
15
20
t
min –3 0
[4] 15 m/min uniform motion in the following acceleration time Q.22. The uniform
is
[1] AB
15 C
a(m/s2 10
[2] BC
D
5
[3] CD
B
A
-5
E 2
4
6
8
10 t
[4] DE
acceleration ion of the particle partic le is Q.23. The displacement-time relationship for a particle is given by x = a0 + a1t + a2 t 2 . The accelerat [1] a 0
[2] a1
[3] a 2
[4] 2a2
particle travels travels for 40 seconds seconds under under the the influe influenc nce e of a constant constant force. If the distanc distance e travelle travelled d by the the particle is Q.24. A particle S1 in the first twenty seconds and S 2 in the next twenty seconds, then [1] S2 = S1
[2] S2 = 2S1
[3] S2 = 3S1
[4] S2 = 4S1
moves with constant constant acceleration acceleration for 6 seconds seconds after st arting arting from fr om rest. The The distance distance travelled travelled durin during g Q.25. A particle moves the consecutive 2 seconds interval are in the ratio [1] 1 : 1 : 1
[ 2] 1 : 2 : 3
[3] 1 : 3 : 5
[4] 1 : 5 : 9
having ng initial initial velocity velocity u is movin moving g with uniform uniform acceleration acceleration a. The The distance cove covered red by it in n Q.26. A body havi
[1] u +
a 2n + 1) 2
[2] u −
a 2n − 1) 2
[3] u −
a 2n + 1 2
[4] u +
a 2n − 1 2
is thrown upward upward and reache reaches s a height height of 64 feet, its initial initial veloci velocity ty shoul should d be (g = 32 ft /sec 2) Q.27. A ball is [1] 64 ft/sec
[ 2] 72 ft/ sec
[3] 32 ft/sec
[4] 4096 ft/ sec
th
second is
M otion in one dimensions dimensions
dif ferent heights, heights, viz a and b. The ratio of times Q.28. Two bodies of different masses m a and mb are dropped from two different taken by the two to drop through these distance is [1] a : b
[ 2]
ma b : mb a
[3]
[4] a 2 : b 2
a: b
stone weighin weighing g 10 kg is dropped from a cliff cliff in a high high wind. The The wind wind exerts exerts a steady horizo horizontal ntal force of 50 N on Q.29. A stone the stone as it falls. The path that the stone follows w ill be be [1] A parabola
[2] An ellipse
[3] A more complicated path
[4] A straight line
up with w ith a finite speed is caugh caughtt back after 4 sec. The The speed of the body with which which it is thrown Q.30. A body thrown up up is [1] 10 m/ sec
[ 2] 20 m/sec
[3] 30 m/sec
[4] 40 m/sec
height on a glass floor so that it rebound rebounds s elastically elastically to the same height. height. If the Q.31. A ball is dropped from certain height process continues, the velocity-time graph for such a motion would be V
V
[1]
[ 2] T
T
2T
2T
[3]
[4] T
t→
t→
2T
T
2T
t→
t→
vertically y upwards with an initial initial veloci velocity ty of 30 m/s. The The time t aken for t he stone stone to rise to its Q.32. A stone is thrown verticall maximum height is [1] 0.326 s
[ 2] 3.26 s
[3] 30.6 s
[4] 3.06 s
upward and reaches reaches its maximu maximum m height. height. At that position Q.33. A body is thrown upward [1] its velocity is zero and its acceleration is also zero [2] its velocity is zero but its acceleration is maximum [3] its acceleration is minimum [4] its velocity is zero and its acceleration is the acceleration due to gravity Q.34. The initial velocity of a particle (at t = 0) is u and the acceleration of particle at time t is given by
f = at. Where a is a constant constant which of the following relation for velocity v of particle after t ime t is true? [1] v = u + at 2
[2] v = u + at 2/2
[3] v = u + at
km/hr. Q.35. A man is walking on a road with a velocity 3 km/hr.
[4] none of these
Suddenly Suddenly rain start s falling. The velocity velocity of rain is
10 km/hr in vertically downward direction. The relative relative velocity of the rain is [1]
13km/hr
[2]
7km/hr
[3]
109 109 km /hr
[4] 13 km/hr
moving at 40 km/hr km/hr and and another another boat Q is movin moving g at 20 km/hr. km/hr. Which Which one one of the following following is not a Q.36. A boat P is moving possible value value for f or their relative relat ive velocity [1] 10 km/hr
[ 2] 20 km/hr
[3] 30 km/hr
given b Q.37. The position of a body with respect to time is given
x = 4t
[4] 40 km/hr 3
– 6t 2 + 20 t + 12.
Acceleration at
t = 0 will be [1] –12 unit s
[2] 12 unit s
[3] 24 units
[4] –24 unit s
travels 200 cm in the first tw o seconds seconds and and 220 220 cm in the next next four second. second. The The velocity velocity at the end end of the Q.38. A body travels seventh second from the start will be [1] 10 cm/s [2] 5 cm/s [3] 15 cm/s [4] 20 cm/s 0 man standin standing g on a road hold hold his his umbrel umbrella la at 30 with the vertical vertical to keep the rain away. He throws the umbrella umbrella Q.39. A man and starts running running at 10 km/h. He finds that raindrops are hitting his head head vertically, the speed of rain drop wit h respect to the road will be [1] 10 km/h
[2] 20 km/h
[3] 30 km/h
[4] 40 km/h
M otion in one dimensions dimensions
varies with w ith time. The equation for variat ion is Q.40. The linear momentum of a body is p. The linear momentum p varies 2 p = a + bt where a and b are constants. The effective force acting on the body is [1] proportional to t 2
[ 2] co constant
[3] proportional to t
[4] inversely proportional to t
increases linearly as bt with wit h time. If the particle start s from v 0 as initial velocity then Q.41. The acceleration of a particle increases the distance travelled in t seconds will be [1] v0 t +
1 3 bt 6
[2] v0 t
−
1 2 bt 6
[3] v0 t −
1 3 bt 6
[4] v0 t +
1 3 bt 2
has velocity velocity given given by by v = 20 + 0.1 t 2 then it has Q.42. A particle has [1] uniform acceleration
[2] uniform retardation
[3] non unif orm acceleration
[4] zero accelerat ion
has uni uniform form acceleration acceleration 8 m/sec 2. The distance travelled by it in 5th second second will be Q.43. A body starting from rest and has [1] 36 m
[ 2] 40 m
[3] 100 m
[4] 200 m
distances travelled travelled by the body body during during 3rd and 4th 4th seconds seconds is Q.44. A body starts from rest, t he ratio of distances [1] 7/5
[ 2] 5/7
[3] 7/3
[4] 3/ 7
sliding on a smooth inclin inclined ed plane plane requires requires 4 sec to reach the bottom bottom after starting from rest at the top. Q.45. A body sliding How much time does it take to cover one fourth the distance starting from the top [1] 1 sec
[ 2] 2 sec
[3] 0.4 sec
[4] 1.6 sec
initial velocity of a particle is 10 m/sec and its retardation ret ardation is 2 m/sec 2. The distance covered covered in the fifth second second Q.46. The initial of the motion will be [1] 1 m
[ 2] 19 m
[3] 50 m
[4] 75 m
moving east-wards with a velocity of 5m/sec. In 10 seconds its velocity velocity changes changes to 5m/sec northnorthQ.47. A particle is moving wards. The average average acceleration during during this time is [1]
1
[3] 1
2
1
m/ sec 2 in N-W direction 2
[2]
m/sec2 in N-W direction
[4] 1
2
m/ sec 2 in the N-E direction 2 m/sec2 towards east
ship of mass mass 3 x 10 7 kg initially at rest, is pulled by a force of 5 x 10 4 N through a distance of 3m. Assuming that Q.48. A ship the resistance due to water is negligible, the speed of the ship is [1] 1.5 m/sec
[2] 60 m/sec
[3] 0.1 m/ sec
[4] 5 m/ sec
Q.49 A part icle moves wit h a constant acceler ation such t ha in t he successive time intervals t
1
, t 2 and t 3 its
average velocities are v 1, v2 and v3. The ratio of of v1 – v2 and v2 – v3 is [1] t1 − t2 : t 2
t
+ 3
[2] t1
t : t2
+ 2
t
[3] t1
+ 3
t : t2
− 2
t
− 3
[4] t 1 – t 2 : t 2 – t 3
tr avels from place A to the place B at 20 km/hou and returns at 30 km/hour. The average aver age speed Q.50 A car travels of the car for the whole journey is [ 1] 2 5 k m/hour
ANSWER KEY Q u s. 1 Ans. 3 Q u s. 16 16 Ans. 1 Q u s. 31 31 Ans. 3 Q u s. 46 Ans. 1
2 1 17 1 32 4 47 1
[ 2] 24 k m/hour
3 1 18 3 33 4 48 3
4 1 19 4 34 2 49 2
5 2 20 3 35 3 50 2
6 4 21 1 36 1
[ 3] 50 km/hour
7 1 22 1 37 1
8 4 23 4 38 1
9 2 24 3 39 2
[ 4] 5 k m/ hour
10 4 25 3 40 3
11 3 26 4 41 1
12 3 27 1 42 3
13 2 28 3 43 1
EXERCISE # 1 14 15 3 3 29 30 4 2 44 45 2 2
M otion in one dimensions dimensions
EXERCI SE # 2 Q.1 Q. 1
The velocity-t velocity-t ime graph of a l inear motion is shown shown be ow. The displacement displacement fr om the origin after 8 seconds is 4 2
s / m0 u
5 6 7 8 1 2 3 4
t(sec)
-2 -4
[ 1] 1 8 m
[ 2] 16 m
[ 3] 6 m
tr ain is moving in the north at a speed 10 m/sec . I Q.2 Q. 2 A train
[ 4] 6 c m length is 150 m.
the tr ain in the south south with a speed of of 5 m/s.
The tim
[ 1] 12 se c
[ 3] 15 se c
[ 2] 8 s e c
A parrot parr ot is flying parallel to
taken by the parro parro t to cross the train will be [ 4] 10 se c
(
par ticle is moving in a plane wit h velocity given by u = u0i + aω cos ωt j , where i and j are unit vectors Q.3 Q. 3 A particle along along x and y axes respectively. respectively. If particle is at the origin origin at t = 0. Calculate Calculate the trajectory of the particle
[1] y Q.4 Q. 4
u0 = a sin ωx
[2] y
= a sin ωx u0
u0 = 1 . sin ωx a
[3] y
[4] y
= 1 . sin ωx a u0
In the following velocity-time graph of a body, the distance and displacement travelled by the body in 5 second in meters will be 40 30 20 10 0
4 1
2
3
5 (sec)
-10 -20 -30
[1 ] 70, 110
[ 2] 11 0, 70
[ 3] 4 0, 7 0
[ 4] 9 0, 5 0
runner complet es one round of a circular pat h of rad s r in 4 0 sec. His displacement displac ement afte r 2 minutes minutes Q.5 Q. 5 A runner 20 sec. will be [ 1] zer o Q.6 Q. 6
[2] 2
πr
[ 3] 2 r
[4 ] 7
πr
The displacement is given by x = 2t 2 + t + 5, the acceleration at t = 5 sec will be [1] 8 m/s 2
[2] 12 m/s 2
[3] 15 m/s 2
[4] 4 m/s 2
Q.7 Q. 7 A p a r t ic le mo ve s a lo ng t he x- a xi s in s uc h a w a y t ha t i s x- c o o r d in a t e va r ie s w it h t im e a s
x = 2 – 5t + 6t 2. The initial velocity velocity and accleration accleration of particle will espectively be [ 1] 1] –5 –5 m/s , 1 2 m/ m/ s Q.8 Q. 8
[ 2] 2] 5 m/ s, s, –1 –12 m/ m/ s
[ 3] 3] –5 –5 m/ m/ s, s, –12 m/ m/ s
[ 4] 4] 5 m/s , 12 12 m/ m/ s
Two trains tra ins each of length length 50 m, are approac hing hing each other other on parallel par allel rails. Their velocities are 10 m/s and 15 m/s. They They will cross each other in [ 1] 2 s e c
[ 2] 4 s e c
tr avels a dista nce of 2000m. Q.9 Q. 9 A car travels
[ 3] 10 se c If the firs t half
[ 4] 6 s e c
istance is covered at 40 km/hour and the second
half at velocity v and if the average velocity velocity is 48 k /hour /hour then the value value of v is [ 1] 5 6 k m/hour
[ 2] 60 k m/hour
[ 3] 50 km/hour
[ 4] 48 k m/hour
M otion in one dimensions dimensions
versus us time t curves. But only some of these can be realised Q.10 The following figures show some velocity V vers in practice. These These are V
V
O
t
O
(a ) [ 1] Only a, b and d
V
V
t
O
O
t
(b )
t
(c )
[ 2] only a , b, c
(d )
[ 3] o nly b a nd c
[ 4] all of t hem
insta nt t, t , the coordi nates of a parti p article cle x = at 2, y = bt 2 and z = 0, then its velocity at the instant t will be Q.11 At an insta [1] t
a2 + b 2
[2] 2t
[3]
a2 + b 2
[4] 2t 2 a2 + b2
a2 + b 2
shows the position of a particle moving moving on the the Q.12 Figure shows
-axis as a function time
[1] the particle has come to rest 6 times
20
e c a l p s i 10 D
[2] the maximum speed is at t = 6 sec [3] the velocity remains positive for t = 0 to t = 6 sec [4] t he average average velocity velocity for the total period show in in
2
egative
rock et is projected projec ted vertically vertical ly upw ards and its time Q.13 A rocket height attained by the rocket is
4
6 t (sec)
locity graph gra ph is shown in t he figure. The maximum
1000
V (M/sec)
[ 1] 1 k m
[ 2] 1 0 k m
20 t(sec)120
[ 3] 10 0 k m
[ 4] 60 k m
dro pped into a well and the sound of impact of stone on the wat er is heard afte r 2.056 sec Q.14 A stone is dropped of the release of stone fro the the top. If acceleration
e to gravity is 980 980 cm/sec
2
and velocity of sound
in air is 350 m/s, calculate the depth of the well [ 1] 1 .96 m
[ 2] 19. 6 m
[ 3] 6.9 1 m
droppe d from a height h under under accelera tion d Q.15 A body is dropped its fall for first half half and the second second half distance, distance, [1] t 1 = t 2
[2] t 1 = 2t 2
[ 4] 69. 1 m
to gravity g. If t
1
and t 2 are time intervals for
e relation betwe en them is
[3] t 1 = 2.414 t 2
[4] t 1 = 4t 2
roc ket is launched launched from fr om the earth eart h surface surfa ce so that it has an acceler ation of 19.6 m/s 2. Q.16 A rocket is swit ched off after 5 seconds seconds of its launch, launch, then th [ 1] 2 45 m
[ 2] 490 m
maximum maximum height attained by by the rocket w ill be
[ 3] 98 0 m
the relation between distance distance x and time t is is denot denot Q.17 If the
If its engine engine
[ 4] 73 5 m
by t = αx2 + βx where α and
β are constant
quantities, the deceleration of the particle is [1] 2 αv 3
[2] βv 3
[3] 2αβv3
par ticle is m oving so that its displacements is given as s Q.18 A particle
[4] 2β2v 3 velocity at the the = t 3 − 6t 2 + 3t + 4 meter. Its velocity
instant when its acceleration is zero will be [ 1] 3 m/ s
[ 2] –12 m/ s
[ 3] 42 m/ s
[ 4] –9 m/ s
M otion in one dimensions dimensions
ca r start sta rts s from fr om rest res t and has an acceler ac celerati ation on a = Q.19 A car 4 m/s. m/s.
moving with a un unifor m velocity of t . A truck is moving
At what distance will the car overtake overtake the tru
? (at t = 0 both start their motion motion in in the same
direction from the same position) [ 1] 1 6 m
[ 2] 8 m
[ 3] 32 m
[ 4] 4 m
releas ed fro m the Q.20 An object is released fro m some height. Exactly afte r one second, another object is released same heigh height. t. The distance betwe en the two objects exa exa ly after 2 secodns secodns of the release of of second object will be [ 1] 4 . 9 m
[ 2] 9. 8 m
[ 3] 19. 6 m
gro und d with a velocity of 80 ft/sec. ft /sec. Q.21 A ball is throw n fr om the groun
[ 4] 24. 5 m Then the ball w ill be at a height height of 96 feet fee t
above the ground after time [ 1] 2 and 3 se c
[ 2] only 3 se c
[ 3] only 2 se c
[ 4] 1 and 2 se c
spee d u and then throw s Q.22 A man st anding on the edge of a cliff throw s a sto ne stra ight up with initial speed another another stone straight down with same same initial initial speed u rom the same same position. Find Find the ratio of speeds, the stone would have attained when they hit the ground at the base of the cliff? [ 1] 2 : 1
[ 2] 1 : 2
[ 3] 1 : 1
dro pped fro m a bridge and it reaches the gr Q.23 A stone is dropped [ 1] 7 8. 4 m
[ 2] 64 m
[ 4] 3 : 1 nd in 4 seconds.
[ 3] 26 0 m
dro pped from fr om the to p of a tow er and i t stri Q.24 A stone is dropped
The height height of the bridge is
[ 4] 200 0 m
s with 3 km/hr against the groun gro und. d. Another stone
is thrown vertically vertically downwards from the same top of th tower with a velocity velocity 4 km/hr. km/hr. Its velocity velocity when it strikes the ground will be [ 1] 7. 0 k m/hr
[ 2] 5. 0 k m/hr
[ 3] 3. 5 k m/hr
[ 4] 4. 0 k m/hr
sto ne is thrown vertically verti cally upwards from fr om the top of a tower tow er with a velocity u and it reaches rea ches the groun gro und d Q.25 A stone with a velocity velocity 3u. The heigh heightt of the tower is
[1]
3u2
g
[2]
4u2
[3]
g
6u2
as a funct funct ion of time i Q.26 The displacement of a part icle as
9u2
g
[4]
shown in fig.
The fig. indicates that
g
y e n a t i D
0
1
2 3 Time
4
x
[1] the particle starts with a certain velocity, but the motion is retarded and finally the particle stops [2] the velocity of particle is constant throught [3] the acceleration of the particle is constant throughout [4] the particle starts with a constant constant velocity, velocity, the with another constant velocity.
tion is accelerated and finally finally the the particle particle moves moves
Q.27 The acceleration of a particle, starting from rest, va ies with time according to the relation a = kt + c. Then the velocity velocity v of the particle after a time t will be
[1] 2kt 2 + ct
[2]
1 2 kt + ct 2
[3] kt 2 + ct
[4]
1 2 kt + ct 2
M otion in one dimensions dimensions
moving in the posit ive dire ion of x-axis varies as v Q.28 The velocity of a part icle moving
=α
x where
α
is positive
constant. Assuming Assuming that that at t he moment t = 0, t he particle particle wa s located at x = 0 t he valu value e of time dependence dependence of the velocity and the acceleration of the particle
[1]
t 2α
2
,
1 2α
[2]
2
α2 t α2 ,
2
[3]
2
2t
α
,
2
2
[4] None of these
α2
points are locat ed at the vertices vertices of a n equil equilateral ateral tr iangle iangle whose side equals a. They all all start Q.29 Three points moving simultaneously with velocity V constant in magnitude. Wit h the first point heading continuously for the second, the second second for the third and and t he third for t he first . How soon will the points coverage? coverage? [1]
3V a
[2]
2a 3V
[3]
a 3V
[4]
a V
respectively. They They reach the ground ground Q.30 Two bodies of masses m 1 and m 2 are dropped from height h 1 and h2 respectively. after time t 1 and t 2 respectively. respectively.
t1 [1] t2
1/ 2
= h1 h2
t1 [2] t2
Which of the following relation is correct
= h1 h2
t1 [3] t2
1/ 2
= m1 m2
t1 [4] t2
= m1 m2
of t he following following stat ements ements is wr ong about about a bal thrown vertically up? Q.31 Which of [a] it is moving with constant acceleration [b] it may have have diffe diffe rent velocities velocities at the same posit n [c] it may have two positions at the same time [d] t he angula angularr momentum of the particle about origin emains conserved conserved [ 1] c onl y
[ 2] c, d
[ 3] b, c , d
[ 4] a, b, c and d
pro jected vertically verti cally upwards upward s and it reaches the maximum maximum height H in time T seconds. Q.32 A part icle is projected
The
height of the particle at any time t will be [1] g t − T
2
[2] H −
1 g t−T 2
)
2
[3]
1 g t−T 2
2
(
[4] H − g t − T
)
roc ket is fir ed vertically verti cally upwards such t hat its engine engine tak es 10 seconds in e xploding xploding fully. Its It s velocity Q.33 A rocket time curve is shown shown in the figure. The height height re ached by the rocket is
s1000 n 500 y500 c 10 20 30 40 50 Time (in sec)
[ 1] 20 kms
[ 2 ] 4 0 k ms
[ 3] 40 0 kms
[ 4] 1000 kms
Q.34 If the displacement of a particle varies with time according to the relation x
= K [1 − exp −bt ] , then the b
velocity (V) of the particle is
[1] V
= K exp (−bt
[2] V
= K exp −bt b
[3] V
=
K2 b
exp( −bt )
[4] V
=
K exp b2
−bt
M otion in one dimensions dimensions
Q.35 If velocity of a particle is given by V
[1] 2 m/s 2
= 10 + 2t 2 m / s .
[2] 4 m/s 2
The average average acceleration betwe betwe en 2 and 5 s is
[3] 12 m/s 2
[4] 14 m/s 2
building 100 m high and buries itself its elf 2 meters deep Q.36 A body of mass 3 kg falls from the multisto reyed building in the sand. sand.
The time of penetra penetra tion will be
[ 1] 9 s ec .
[ 2] 0. 9 s ec .
[ 3] 0.0 9 s ec .
tr avelling ng w ith unifor m acce lera tion cr osse s tw Q.37 A bod y travelli
[ 4] 10 s ec.
point s A and B wit h veloci ties 20 m/sec m/ sec and
30 m/s m/s ec respect ively. ively.
Then Then the speed of of the body at
[ 1] 25 m/ se c
[ 2] 25.5 m/ se c
d-point of A and B is
[ 3] 2 4 m/ se c
[4] 10 6 m/sec
mounted vertically, are made to move towards each other wit h a speed v m/s each. A particle that can Q.38 Two mirror s, mounted bounce bounce back between the two mirrors starts start s from one mirror when the mirrors are d meters aprat. On reaching reaching the second mirror, it bounces bounces back and so on. If the t he particle keeps on travelling at a constant constant speed of 3 v m/s, how many trips can it make before the mirrors run into each other and what total distance does it cover [1]
∞,5.1d
[2]
∞,1.5d
[3] 0,6.1d
[4] 0,1.6d
tra ins each each having having a speed speed of 30 km/hour are headed at each other on the same straight tr ack. A Q.39 Two trains bird that can fly at 60 km/hour km/hour flies off off from one tra when they they are 60 km apart and heads heads directly for the other other tr ain. ain. On reaching reaching the other other tr ain itit f lies directly directly back t o the first, and so fourth fourth then the the total distance travelling by the bird is [ 1] 40 km
[ 2] 6 0 k m
[ 3] 8 0 k m
[ 4] 10 0 k m
distance covered covered by the body in time 't' is propor onal onal to the square of the time 't'. The acceleration acceleration Q.40 The distance of the body is [ 1] inc r ea s ing
[ 2] dec reas ing
[ 3] zer o
Q.41 If the displacement of a particle varies with time as
[ 4 ] co ns tant
= t +7 ,
x
the
[1] [1 ] velocity velocity of the the particle particle is inv inversel ersely y porportion porportional al to t [2] velocity veloc ity o f the pa rticl rt icle e is propor pro por tional t o t [3] velocity of the particle is proportional to
t [4] the particle moves with a constant acceleration
ions a train accelerates uniformly uniformly at Q.42 Between two stat ions retards uniformly uniformly.. If the ratios of time taken are 1 the average speed over the whole journey [ 1] 45 km/hr
[ 2] 5 4 k m/hr
fr om rest at a constant rat e Q.43 A car acceler ates from rate
[1]
β
to come to rest.
αβ V =t α −β
rst, t hen moves moves with constant constant speed and and finally finally
8 : 1 and and the greatest speed is 60 km/hour. km/hour. Then
[ 3] 3 5 k m/hr
α
for some time aft er which it decelera tes at a constant
The maximum maximum velocity V reached if t
[2] V
β2 α − β
= t
[ 4] 53 k m/hr
[3] V
al time taken (t seconds) is given by
α2 α + β
= t
[4] V
αβ = t α +β + β
Q.44 The distance x travelled by the car in above problem in time 't' is given by
[1]
αβ x= 2 α −β t2
[2]
αβ x=t α + β 2
[3]
α+β x=t α −β − β 2
[4] x
αβ = 2 α +β t2
bal l is thr ow n vertic ver ticall ally y upw ar ds w ith it h a velocit velo city y of 30 m/s. m/ s. If the accel ac cel er atio n due to gravit gra vity y is Q.45 A ball 2 10 m/s , what w ill be the distance distance tr avelled avelled by it in the las las second of motion. [ 1] 5 m
[ 2] 10 m
[ 3] 25 m
[ 4] 30 m
M otion in one dimensions dimensions
differ ent heigh heights. ts. One ball is dropped 2 sec after the other but they both Q.46 Two balls are dropped f rom differ strike the griound griound at the same same time, 3 sec after t he f st is dropped. The difference in the the heights heights at which they were dropped is [ 1] 7 . 8 m
[ 2] 78 m
travels half half its total path in in the last last seco Q.47 If a body travels [ 1] 1] 3. 3. 41 41 se c , 57 m
[ 2] 2] 4. 4. 31 31 se c , 57 m
[ 3] 15. 6 m
of it s fall from rest then the time time and and height height of its fall are [ 3] 3] 1. 1. 34 34 se c, 57 m
high, a stone is thrown Q.48 From the foot of a tow er 90 m high,
[ 2] 38. 6 m
[ 4] 4] 3. 3. 14 14 se c , 7 5 m
so as to reach the top of of the tow er. Two second
later another stone stone is dropped dropped from the top of the tower. [ 1] 8 3. 6 m
[ 4] 39. 2 m
The two stones will meet at
[ 3] 63. 8 m
[ 4] 68. 3 m
upward, w ith the the same initial velocity velocity of 98 m/s but 4 sec apart. How Q.49 Two bodies are thrown vertically upward, long after the first one is thrown will they meet? [ 1] 10 se c
[ 2] 11 se c
[ 3] 12 se c
throw n vertically verti cally upwards from fr om the top of a Q.50 A ball is thrown
[ 4] 13 se c
wer with a velocity of 10 m/sec.
If the ball falls
on the ground after 5 seconds, the height of the tower will be [ 1] 2 5 m
[ 2] 50 m
[ 3] 75 m
[ 4] 10 0 m
Q.51 In the above question, what height above the tower will the ball attain?
[1]
5 m
[ 2] 5 m
[3 ] 5 2 m
[ 4] 10 m
Q.52 In the above question, the total distance travelled by the ball before it returns to the ground is
[ 1] 8 5 m
[ 2] 75 m
[ 3] 10 0 m
question, in what time will it reach the Q.53 In the above question, [ 1] 1 s e c
[ 2] 2 s e c
[3 ]
[ 4] 17 5 m
aximum aximum height
2 se c
[4] 1/
2 sec
above question, with what velocity velocity will the bal strike the ground Q.54 In the above [ 1] zer o
[ 2] 40 m/ s
[ 3] 10 m/ s
dro pped fro m the top of the tow er and tra ve Q.55 A stone is dropped height of the tower is [ 1] 4 4. 1 m
[ 2] 49 m
[ 4] 60 m/ s
24.5 24. 5 m in the last second of its journey. journey. The
[ 3] 78. 4 m
[ 4] 72 m
dropped from the same point point after an int val of 1 s. If acceleration due due to gravity gravity is 10 Q.56 Two balls are dropped 2 m/s , what will be the separation 3 seconds after the release of first ball? [ 1] 5 m
[ 2] 10 m
[ 3] 25 m
[ 4] 30 m
interval of 2 s econds. econds. Q.57 Two balls of equal masses are thrown upwards along the same vertical direction at an interval With the same initial initial velocity of 39.2 m/sec. [1 ] 11 7. 6 m
[ 2] 73. 5 m
Then these collide at a height height of [3] 196. 0 m
[ 4] 44. 1 m
Q.58 The speed v of a particle movign along a straight line, when it is at a distance x from a fixed point on the line is given by v 2 = 108 x – 9x 2 . Then Then magnitude magnitude of its its accelera tion w hen it is at a istance 3 metre
from the fixed point is [1] 9 m/s 2
[2] 18 m/s 2
[3] 27 m/s 2
[4] None of these
to the lift and the time of flight is found to be 't' . Q.59 A body is thrown up in a lift with a velocity u relati The acceleration with which the lift is moving up will be [1]
u − gt t
[2]
u + gt t
[3]
2u − gt t
[4]
2u + gt t
M otion in one dimensions dimensions
dro pped from fr om the top of a tow er covers 7/16 of Q.60 A body dropped time of fall is [ 1] 2 s e c
[ 2] 4 s e c
e tota l height height in t he last second of its fall. The
[ 3] 1 s e c
[4 ]
50 sec 7
p article cle Q.61 A perso n standing on the roof of a house of height h throws a particl e vertically d ownwar ds and other parti in a horizon horizontal tal direction with the same speed u. u. The tio of speeds of the particles on reachin reaching g the earth is [1]
2gh :u
[ 2] 1 : 2
[3 ]
above question, question, the ratio of vertical component component Q.62 In the above [1 ] one
[ 2] mor e t ha n one
[4] 1 : 1
2 :1
of the velocities velocities will be
[ 3] les s tha n o ne
[ 4] will de pend o n mas s
Q.63 In the above question the first particle instead of being thrown downwards, is thrown upwards with the
same velocity. velocity.
The ratio of t he velocities of the par icles on reachin reaching g the earth, will be
[ 1] 1 : 1
[2]
2 :1
[ 3] 2 : 1
[ 4] 1 : 4
continuo ly such that each ball att ains 20 m height. height. When Q.64 Juggler keeps on moving four balls in the air continuo the first ball leaves leaves his hand, the position position of the ot r balls ( in metre height) will be [ 1] 10, 20, 1 0
[ 2] 15, 20, 1 5
[3] 5, 5 1, 2 0
[4] 5, 1 0, 2 0
Q.65 The retardation of a motor boat after its engine is sw ched off, is given by
constant and v 0 is its velocity at the time of shutting shutting off of the en ne. after time t will be
v0 [1]
[2] v0e −kt
2v kt + 1 2 0
[3]
v0 2
dv = – kv30, where k is a dt
The velocity velocity of the motor boat
[4] v0
Q.66 A p a r t ic le mo ve s w it h c o ns t a nt s p e e d v a lo ng a r e g ul a r he xa g o n AB C DE F in s a me o r d e r (ie., A to B, B to C, C to D, D to E, E to F, F, F to A.. ) Then magnitude magnitude of average average velocity for its motion from A to C
[ 1] V
[ 2] V/ 2
[3 ]
[4] None of these
3V/2
acceleration ( a) of m oving oving particle varies with displacement displacement according to t he following relation a Q.67 The acceleration Then correct r elation betwe betwe en velocity velocity and displacemen displacemen is (where C = constant)
x3 3
3x 2 + 2
[1] V
=
+C
[3] V
= 2 x3 + 3 x2 + C 3
[2] V
=
2 3 x 3
= x2 + 3 x .
+ 3x 3x 2 + C
[4] V = 2x + 3
moves in a straight line in such such a mann manner er t t its reta rdation is is proport ional ional to its speed, the Q.68 If a point moves distance covered (x) is assosciated with speed (V) is [1] x
∝V
[2] x ∝ V 2
[3] x ∝ V3
[4] x
∝ −V
rebounds wi th a velocit y which is 3/4 th of the velocity wit h which Q.69 A ball is d ropped f rom a height o f 20 m a nd rebounds it hits the ground. What is t he time interval betw een the first and second bounces bounces (g = 10 m/s 2 ) [ 1] 3 s e c
[ 2] 4 s e c
[ 3] 5 s e c
[ 4] 6 s e c
M otion in one dimensions dimensions
fr om w est to east at a speed of 5 metres /minute. Q.70 A river is flow ing from river, capable capable of swimming swimming at 10 metres/ metres/ min. min. in still time.
A man on the south sout h bank of the
ater, wants to swim across the river in in shortest
He should swim in a direc tion [ 2] 30 0 ea st st of of no no rt rt h
[ 1] d ue no rt h
[3 ] 30 0 wes west of north orth
[4] [4] 60 60 0 east of north
uniform m speed v Afte r it has made an angle of 60 0, the change in its Q.71 A part icle moves along a circle w ith a unifor speed will be
[1] v 2
v
[2]
[3] v 3
2
[4] 0
t o wat er a velocity which is 1/n times the river flow velocity. At what angle to the Q.72 A boat moves relat ive to stream direction must be boat move to minimize drifting? [1]
−1
π/2
[2] sin
1 n
[3]
Q.73 A part icle moves w ith a v in a horizontal ci rcular p at
[1] v 2
[2] v / 2
π 2
+ sin−1
1/ n
[4]
π 2
− sin−1
Q.74 A car A is goving nor th-east at 80 km/hr. and antoher
[1 ] 1/ 7
[4] 3/ 5
[3] 4/ 3
[1] aω
and y
= a sin ωt .
tan α is
The acceleration of particle is
[3] –aω 2
[2] a 2ω
will be
ar B is going south-east at 60 km/hr. Then the
α such that
= a cos ωt
0
[4] v
direc tion of the velocity of A relati ve to B makes with the north an angle
of p article is defined by x Q.75 The motion of
)
The change in its velocity f or covering 60
[3] v 3
[ 2] 3/ 4
1/ n
[4] a 2 ω2
bo at f rom P to a point Q just Q.76 A boa t man could ro w his boat wit h a speed 10 m/sec . He wa nts to t ake his boat opposite on the other other bank bank of the river river flowing at a s ed 4 m/sec. He shou should ld row his his boat [1] at right angle to the stream −1
[2] at an angle of s in
(2 / 5
(2 / 5 − [4] at an angle angle of cos (2 / 5 −1
[3] at an angle angle of s in
1
Q
with PQ up the stream Vs =4m/s 4m/s
with PQ down the stream P
with PQ down the stream
completi ng half the ci rcle, Q.77 A part icle is executing a circular mot ion of r adius R th a uniform speed v. Aft er completing the change in velocity and in speed will be respectively [ 1] zer o, zer o
[2] 2 v, zer o
[ 3] 2 v, 2 v
[4] ze ro , 2 v
height of 81 metre s and is ascending upwards upwar ds wit h a velocity of 12 m/s . A body of 2 kg Q.78 A balloon is at a height 2 weight is dropped from it. If g = 10 m/s , the body w ill reach the surface of t he earth in [1 ] 1. 5 se c
[ 2] 4. 025 se c
[3] 5. 4 se c
[ 4] 6 .75 se c
→
Q.79 If the position vector of a particle is r = 3t ˆi − 4 jˆ + kˆ , the particle will be
[ 1] moving with unif orm veloc it y
[ 2] s tat ionar y
[ 3] 3] moving with unif orm a cceler at at io io n
[4] insuff ic ic ie nt da dat a
Q.80 A bullet lo ses
1 20
of its velocity in passing through a plank. The least number of planks required to stop the
bullet is [ 1] 10
[ 2] 11
[ 3] 1 2
[ 4] 2 3
M otion in one dimensions dimensions
Q.81 The motion of a body falling from rest in a resisting medium is described by the equation
dv dt
= a − bv , where
a and b are constants. The velocity at any time t is -
[1] v t
=
a b
(1 − e
−bt
)
[2] v t
=
b a
e
−bt
[3] v t
=
a b
(1 + e
−bt
)
[4] v t
=
b a
e
bt
throw n vertically ver tically upwards. It was observed a a height height h t wice wit h a time interval Q.82 A ball is thrown
∆t.
The initial
velocity of the ball is -
[1]
8gh + g (∆t) 2
[2]
2
8gh +
g∆t 2
2
[3]
1 2
8gh + g ( ∆t ) 2
2
[4]
8gh + 4g2 (∆t )2
O . It passes t hrough he points P, P, Q, R .. .... .. .... such that OP, OP, OQ , OR,. OR ,... .... are Q.83 A stone falls free ly f rom a point O. in geometric progression. Then velocities of stone at P, Q, R.... are in [ 1] a rithmetic pr ogre ss ion
[2] ge omet ric pr og re ss ion
[ 3] har mo nic pr ogre ss ion
[ 4] log ar it hmic mean
Q.84 A ship of mass 3 × 10 7 kg, initially at rest, is pulled by a force of 5 × 10 4N through a distance of 3m.
Assuming Assuming that the resist ance due to wate r is negligibl [1] 1.5 ms –1
[2] 60 ms –1
the speed of the ship is -
[3] 0.1 ms –1
Q.85 An elevato r whose floor to ceilling distance is
l is
[4] 5 ms –1
a scending w ith unifor uniform m accelera tion i t. At some in ant
(say t = 0), a loose bolt drops from its ceiling. The time taken by the bolt to hit the floor is -
2l g −a
[1]
[2]
2l g
2l g +a
[3]
[4]
2l a
ANSWE ANSWER R KEY KEY
Q u s. Ans. Q u s. Ans. Q u s. Ans. Q u s. Ans. Q u s. Ans. Q u s. Ans.
1 3 16 16 4 31 31 1 46 46 4 61 61 4 76 2
EXERCISE # 2
2 4 17 1 32 2 47 1 62 2 77 2
3 2 18 4 33 1 48 1 63 1 78 3
4 2 19 1 34 1 49 3 64 2 79 1
5 1 20 4 35 4 50 3 65 1 80 2
6 4 21 1 36 3 51 2 66 3 81 1
7 1 22 3 37 2 52 1 67 2 82 3
8 2 23 1 38 2 53 1 68 4 83 2
9 2 24 2 39 2 54 2 69 1 84 3
10 1 25 2 40 4 55 1 70 1 85 3
11 2 26 1 41 4 56 3 71 4
12 1 27 2 42 2 57 2 72 3
13 4 28 2 43 4 58 3 73 4
14 2 29 2 44 4 59 3 74 1
15 3 30 1 45 3 60 2 75 3
M otion in one dimensions dimensions
E X E R C I SE SE # 3 Q.1
The displacement time graph for two particles A and B are straight lines inclined at angles of 30 B
time axis. axis. The ratio of velocity velocity of V A : VB is
0
and 600 with the [CPMT-1990]
A [1] 1 : 2
[ 2] 1:
[3]
[4] 1 : 3
3 :1
3
s 600
O Q.2
) ) 30
0
t
An elevator elevator car, car, whose floor to celling celling distance is equal equal to 2.7 m, start s ascending ascending with constant constant acceleration acceleration of of 1.2 ms-2. 2 sec after the start, a bolt begins begins falling from the ceiling ceiling of the car. car. The free fall time of the bolt is [CET Karnataka-94] [1]
Q.3
[2]
0.54 0.54 s
6s
[3] 0.7s
[4] 1s
A body body 'A' is dropped dropped vertically vertically from the the top of a tower. If another another identical identical body body 'B' is projected projected thrown from the the same point at the same instant, then [1] 'A' will reach the ground earlier than 'B' [2] 'B' will reach the ground earlier than 'A' [3] Both 'A' and 'B' will reach the ground simultaneously [4] none of these
Q.4
A body is dropped dropped from the the top of a tower with zero zero velocity velocity and and reaches reaches ground ground in in 4 seconds. seconds. The The heigh heightt of the 2 tower is about [g = 10 m/s ] [AFMC-94] [1] 20 m
Q.5
[ 2] 40 m
[3] 80 m
[4] 160 m
The time displacement graph of a moving particle is shown as the instantaneous velocity is negative of the point [1] D
[AFMC-94; CBSE-94] N E M E C A L P S I D
[2] F [3] C [4] E
Q.6
F C
E TIME
A balloon is is at a heigh heightt of 81 m and is ascendin ascending g upwards with a velocity velocity of 12 m/s. A body of 2 kg weight is 2 dropped from it. If g = 10 m/s m/s , the body will reach the surface of the earth in [1] 1.5 s
Q.7
D
[2] 4.025 s
[3] 5.4 s
[4] 6. 75 s
The initial initial velocity of a body moving moving along a straight line is 7 m/s. It has a uniform acceleration of 4 m/s 2. The distance covered by the body in the 5 th second of its motion is [1] 25 m
Q.8
[RPMT-94]
[ 2] 35 m
[3] 50 m
[RPMT-94]
[4] 85 m
A body is projected projected up to with a speed 'u' 'u' and the time taken by it is T to reach the maxi maximu mum m heigh heightt H. Pick out out the correct statement
[EAMCET-95]
[1] It reaches H/2 in T/2 sec
[2] It acquires velocity u/2 in T/2 sec
[3] Its velocity is u/2 at H/2
[4] Same speed at 2T
M otion in one dimensions dimensions
Q.9
A particle movi moving ng with a uniform uniform acceleration acceleration travels travels 24 m and and 64 m in the first two consecuti consecutive ve interv intervals als of 4 sec each. Its initial velocity is [MP PET-95] [1] 1 m/ sec
[2] 10 m/sec
[3] 5 m/sec
[4] 2 m/ sec
h' s sur f ac e suc h t hat it c re at es a n ac ce le ra ti on o f Q.10 A ro ck et i s fi re d upw a rd f ro m th e ea rt h's 19.6 m/sec 2. If after aft er 5 sec its engine engine is switched switc hed off, the maximu maximum m height height of the rocket fr om earth's surface would be [MP PET- 95] [1] 245 m
[ 2] 490 m
[3] 980 m
[4] 735 m
is thrown upwards upwards with a veloci velocity ty of 100 m/sec. m/sec. It will w ill reach reach the the ground ground after after Q.11 A ball is [1] 40 sec
[2] 20 sec
increasing linearly Q.12 The acceleration of a particle is increasing
[3] 10 sec
[AFMC-95]
[4] 5 sec
time t as bt. The particle starts start s from the origin with an
initial velocity velocity v0. The distance travelled by the the particle in time t will be [1] v0 t +
1 3 bt 6
[2] v0 t
+
1 3 bt 3
[BHU-95,CPMT-95]
1 2 bt 3
[3] v0 t +
[4] v0 t +
1 2 bt 2
proport ional to the t he cube of time passed. The magnitude of the acceleration acceleratio n Q.13 The displacement of a body is given to be proportional of the body, is
[AIIMS-96]
[1] Increasing with time
[2] Decreasing with t ime
[3] Const ant but not zero
[4] Zero
and moves moves with uniform uniform acceleration acceleration.. Then Then the ratio of distance distance covered covered in in n th sec. to n Q.14 A particle starts from rest and sec. is [RPET-96]
[1]
n2
2 1 − [2] n n2
2n − 1
[3]
n2 n +1
[4]
2n + 1 n2
car moves for half half of its t ime at 80 km/h and and for rest half of time at 10 km/h. km/h. Total distance distance covered covered is 60 km. Q.15 A car What is the average speed of the car [RPET-1996] [1] 60 km/h
[2] 45 km/h
[3] 120 km/h
[4] 180 km/h
heightt h with initial initial veloci velocity ty zero, strikes the ground ground with velocity velocity 3 m/s. Anothe Anotherr body of Q.16 A body dropped from a heigh same mass is dropped from t he height height h with w ith an initial initial velocity velocity of 4 m/s. Find the final final velocity with which it strikes the ground [CPMT-96] [1] 3 m/ s
[ 2] 4 m/s
[3] 5 m/s
[4] 12 m/s
Q.17 If a body starts from rest and travels 1.2 m in the 8th second then what is the acceleration
[1] 0.20 m/s 2
[2] 0.16 m/s 2
[3] 0.08 m/s 2
is movin moving g with uniform uniform veloci velocity. ty. Sudden Suddenly ly,, a Q.18 A train is
[AFMC-97]
[4] 0.2255 m/s 2 and still still train is is movin moving g with same
velocity the compartment moves to a ceratin distance dist ance and and comes to rest . The The distance dista nce travelled tr avelled by the compartment is how much times of the distance travelles by the train in the same time [1] one f ourth
[ 2] Half
[3] Equal
[RPET-97]
[4] In uncertain ratio
stone dropped from a buildi building ng of height height h and and it reaches reaches after t second seconds s on earth. From the same same buildi building ng ifif two Q.19 A stone stones are thrown [one upwards and other downwards] with the same velocity u and they reach the earth surface after t 1 and t 2 seconds respectively, then
[1] t
t
t
= 1 − 2
[2] t =
t1 + t2 2
[CPMT-97]
[3] t =
t1t 2
[4] t = t12t 22
M otion in one dimensions dimensions
Q.20 By which velocity a ball be projected vertically so that the distance it covers in its 6 second is twice the distance it covers in its 6 th second -(g = 10 m/s 2) [CPET-2002,CPMT-97]
[1] 58.8 m/s
[ 2] 49 m/s
[3] 65 m/s
[4] 17.5 m/s
and y = bt 2 . The speed of the the particle at Q.21 The coordinates of a moving particle at any time are given by x = at 2 and any moment is [1] 2t a + b]
[EAMCET-93, CPMT-97]
[2] 2t a2 − b2
[3] t a2 + b2
[4] 2t
a2 + b2
experience ce a constant constant acceleration acceleration for 20 sec after start ing ing from rest. If it travels a distance distance S Q.22 A particle experien first 10 sec and a distance S 2 in the next sec, then
[1] S1 = S 2
[2] S1 =
S2 3
1
in the
[CPMT-97]
[3] S1 =
S2 2
[4] S1 =
S2 4
sliding on a smooth inclin inclined ed plane plane requires requires 4 seconds seconds to reach the bottom, starting from r est at the top. Q.23 A body sliding How much time does it take to cover one-fourth the distance starting from rest at the top [1] 1 sec
[ 2] 2 sec
[3] 4 sec
[BHU-98]
[4] 16 sec
released from a great heigh heightt falls falls freely towards earth. Another nother body is released released from the the same same heigh heightt exac exactly tly Q.24 A ball released one second second later. The separation between the two bodies after tw o second the the release of the second body is [BHU-98]
[1] 9.8 m
[ 2] 49 m
[3] 24.5 m
[4] 19.6 m
moving g with a speed of 40 km/hr can be stopped by applying applying breaks aft er atleast 2m. If the same same car is Q.25 A car movin moving moving with a speed of 80 km/h. What is the minimu minimum m stopping distance [CBSE-98] [1] 8 m
[ 2] 2 m
[3] 4 m
[4] 6 m
car t ravels ravels half half distance distance with 40 km/hr km/hr and rest half half distance distance with 60 km/hr., km/hr., then the the average average speed of of car is Q.26 A car [1] 40 km/hr
[ 2] 48 km/hr
[3] 52 km/hr
[4] 60 km/hr
[RPET-98]
moves along along a straight straight line line whose whose equation equation of motion is given given by by s = 12t + 3t 2 − 2t 3 , where[s] is in metres Q.27 A car moves and [t] in seconds. The velocity of the car at start will be [1] 7 m/ s
[ 2] 9 m/s
[3] 12 m/s
[CPMT-98]
[4] 16 m/s
stone is thrown thrown with an initial initial speed of 4.9 m/s from a bridge bridge in verticall vertically y upward upward direction direction.. It falls down in in water Q.28 A stone after 2 sec. The height height of the bridge is [1] 4.9 m
[ 2] 9.8 m
[AFMC-99]
[3] 19.8 m
[4] 24.7 m
initially at rest. Now car A starts start s moving moving with a constant constant velocity of 40 m/s and car B starts Q.29 Two car A and B are initially moving with constant acceleration of 4 m/s 2. How much much time will have have lapsed from before the cars again meet [RPET-99] [1] 15 second
[ 2] 20 second
[3] 30 second
[4] 35 second
wheel covers covers a distance distance of 9.5 km in 2000 revol revolutio utions. ns. The The diameter of the wheel wheel is Q.30 A wheel [1] 15 cm
[ 2] 7.5 cm
[3] 1.5 m
[RPMT -99]
[4] 7.5 m
long are travellin t ravelling g in opposite with velocity of 15 m/s. The time of crossing cr ossing is is [ CPMT -99] Q.31 Two trains, each 50 m long
[1] 2 s
[2]
10 s 3
[3] 2 3 s
[4] 4 3 s
M otion in one dimensions dimensions
displacement of a particle par ticle is given by y = a + bt + ct 2 − dt 4 . The initial velocity velocity and acceleration are respectively Q.32 The displacement [1] b,–4d
[2] –b, 2c
[3] b, 2c
[4] 2c, –4d
[CPMT-99]
stone is allowed allowed to fall from from the top of a tower and and covers covers half half the heigh heightt of the tower in in the the last secon second d of Q.33 A stone its journey. journey. The time taken by the stone to reach the foot of the tower tow er is [1] 2 −
2 s
[2] 2 +
2 s
[CPMT-99]
[3] 4s
[4]
2± 2 s
vertically y upward and it rises through through 20 m and returns returns to t o his his hands. hands. What What was the initial initial Q.34 A man throws a ball verticall velocity (u) of the ball and for how much time (T) it remained in the air (g = 10 m/s 2) [1] u = 10 m/s, T = 2s
[ 2] u = 10 m/s, T = 4s
[3] u = 20 m/ s, T = 2s
[MPPET-2001]
[4] u = 20 m/s, T = 4s
balloon starts rising rising from fr om the the ground ground with an acceleration acceleration of of 1.25 m/s 2. After 8s, a stone is released from the Q. 35 A balloon balloon. balloon. The stone will ( taking g = 10 ms -2)
[Karnataka-2001]
[1] Have a displacement of of 50 m
[2] Cover a distance of 40 m in reaching the ground
[3] Reach the ground in 4s
[4] Begin to move down after being released
very large number number of balls are thrown verticall vertically y upwards in qui quick ck succession succession in in such such a way that the next next ball is Q. 36 A very thrown throw n when the previous one is at the maximum maximum height. height. If the t he maximum maximum height is 5m, the num number ber of balls thrown t hrown -2 per minute is (take g = 10 ms ) [Karnataka-2002] [1] 120
[ 2] 80
[3] 60
[4] 40
is 5 m/s 2, then calculate the distance travelled in the 18th sec Q. 37 Initially a body is at rest. If its acceleration is [1] 86.5 m
[ 2] 87.5 m
[3] 88 m
[4] 89 m
[AFMC-2001]
moving g with velocity velocity 5 m/s towards east and and its velocity velocity chang changes es to 5 m/s north north in 10 sec. sec. Find Find the Q.38 A particle is movin acceleration.
[1]
2N−W
[UP-CPMT-2001]
[2]
1 2
N−W
[3]
1 2
N −E
[4]
2 N −E
stone is dropped dropped from a runni running ng bus. bus. It will travel towards the the ground ground in in a Q.39 A stone [1] st raight line
[2] circular path
[3] parabolic pat h
applied ed on a body of mass 100 kg Q.40 A force of 1000 N is appli
[BHU-2000]
[4] none of these
a velocity velocity of 5 m/s. How How much time time does it
require to acquire a velocity of 25 m/s [1] 2 sec
[ 2] 4 sec
[Manipal-2000]
[3] 6 sec
[4] 8 sec
Q.41 If a freely falling body travels in the last second, a distance equal to the distance travelled by it in the first three
seconds, the time of its travel is [1] 3 sec
[ 2] 4 sec
[Manipal-2000]
[3] 5 sec
[4] 6 sec
packet is dropped dropped from a balloon balloon which is goin going g upward with a velocity velocity 12 m/sec. m/sec. The The veloci velocity ty of the the packet after Q.42 A packet 2 seconds will be [Manipal-2000] [1] –7.6 m/ sec
[ 2] 7.6 m/sec
[3] 12 m/sec
[4] –12 m/sec
Q.43 If a ball is thrown vertically upwards at 40 m/s, its velocity after two seconds will be
[1] 10 m/s
[ 2] 20 m/s
[3] 30 m/s
Q.44 Velocity-time curve for a body projected vertically upwards is
[1] Ellipse
[ 2] Parabola
[3] Hyperbola
[AIIMS 2000]
[4] 40 m/s [AIIMS-2000]
[4] Straight line
M otion in one dimensions dimensions
moving g with a velocity velocity 80 km/hr ahead a car movin moving g with a velocity velocity of 65 km/hr in the same Q.45 A motorcycle is movin direction. What is the the relative velocity velocity of the motorcycle with w ith respect to t o the car [AFMC-2000] [1] 15 km/hr
[ 2] 20 km/hr
[3] 25 km/hr
[4] 145 km/hr
and has an acceleration acceleration 20 cm/sec 2. What is the distance distance covered by the body in Q.46 A body starts from rest and first 8 sec
[AFMC-2000]
[1] 160 cm
[ 2] 640 cm
[3] 1280 cm
[4] 1640 cm
cross es a river of widt h 1 km along along the shortest possible path in Q.47 The speed of a boat is 5 km/hr in still water. If it crosses 15 minutes, then velocity of the river is [AFMC-2000] [1] 4 km/hr
[ 2] 3 km/hr
[3] 2 km/hr
[4] 1 km/hr
travels 10 m in first 5 sec and 10 m in next next 3 sec. Assumin Assuming g constant constant acceleration acceleration what is the the distance distance Q.48 A particle travels travelled in next 2 sec [1] 8.3 m
[RPET-2000]
[ 2] 9.3 m
[3] 10.3 m
[4] None of these
Q.49 The displacement [s] of a body is directly proportional to the square of the time [t] than the acceleration of
the body is
[RPMT-2000]
[1] increases
[ 2] constant
[3] decreases
[4] zero
distance and stops w hen hen applied applied the breaks. If the velocity velocity of train is is just doubled doubled and Q.50 A train covers 50 metre distance applied the same retarding force then the distance covered by the train is [RPMT-2000] [1] 50 m
[ 2] 100 m
[3] 150 m
Q.51 Equation of position [x] with time [t] is given by equation x = 3t
[1] 18 m/s 2
[2] 32 m/s 2
3
[4] 200 m
+ 7t 2 + 5t + 8. The accelerat ion at time t = 1s. is is [4] 14 m/s 2
[3] Zero
[CPMT-2000]
vertically from a height height d above the ground. ground. It hits hits t he ground ground and bounce bounces s up vertically vertically to a Q. 52 A ball is dropped vertically height height d/2. Neglecting Neglecting subsequent subsequent motion and air air resistance, its velocity v varies varies with the height height h above the the ground as [IIT-2000] v
v
d
[1]
h
[2]
v
d
h
[3]
v
d
h
d
[4]
h
moves according according to above above veloci velocity ty time graph. graph. Then Then what is the the ratio between between distance distance travelled travelled in last last Q.53 A particle moves 2 seconds and 7 second
[RPET-2001]
1 [1] 4 [3]
1 [2] 2
1 8
[4]
1 6
m/sec 10
1
3
5
7 sec
Q.54 For a freely falling body ratio of distances travelled in first, second and third second of its motion will be [RPET-2001]
[1] 5 : 3 : 1
[ 2] 1 : 4 : 9
[3] 1 : 3 : 5
[4] 9 : 4 : 1
opposite direct ion with velocity velocity of 10 m/s m/ s and 15 m/s respectively r espectively.. Then Q.55 50 m long trains are crossing each other in opposite time-taken by trains to cross each other will be [1] 2 sec
[ 2] 4 sec
[RPET-2001]
[3] 6 sec
[4] 8 sec
M otion in one dimensions dimensions
move s in e ast wi th velo cit y of 15 m/s m/ s fo r 2 sec. se c. t hen moves nor thw ar d w ith it h 5 m/s m/ s fo r Q.56 A par ti cle moves 8 sec, then average velocity of the particle is [RPMT-2001] [1] 1 m/ s
[ 2] 5 m/s
[3] 7 m/s
[4] 10 m/s
is thrown thrown verticall vertically y upward. Its velocity velocity at half half of the heigh heightt is 10 m/s, m/s, then maxi maximu mum m heigh heightt attained by by Q.57 A particle is 2 it (g = 10 m/s ) [CPMT-2001] [1] 8 m
[ 2] 20 m
[3] 10 m
[4] 16 m
acceleration a = 2[t 2[ t – 1] then its velocity velocity after 5 seconds will be Q.58 A body starts from rest with acceleration [1] 15 m/s
[ 2] 25 m/s
[3] 35 m/s
[RPET-2002]
[4] 45 m/s
point P consider consider at contact contact point point of a wheel on ground ground which rolls on ground ground without without sliping sliping then value value of Q.59 A point displacement of point P when wheel completes half of rotation - [If radius of wheel is 1 m] [1] 2 m
[3] p m
2
[ 2]
p + 4 m
[4]
[CPMT-2002] 2
p + 2 m
moving g with a speed of 50 km/hr km/hr.. can be stopped by brakes brakes after at least 6 m. If the same same car is movi moving ng at Q.60 A car, movin a speed of 100 km/hr, the minimum stopping distance is [1] 24 m
[ 2] 6 m
[CPET-2003]
[3] 12 m
[4] 18 m
moving particle part icle at any time 't ' are given by x Q.61 The coordinates of a moving
3 the particle = a t3 amd y = b t . The speed of the
at time 't' is given by
[CPET-2003]
[1] t2 α2 + β2
α2 + β2
[2]
[3] 3t α 2 + β 2
[4] 3t 2 α 2 + β 2
it h the same sam e spe ed ver ti cal ly upw a ds o ne af te r the ot her at an inte rva l of Q.62 A ma n thr ow s bal ls w ith 2 seconds. What should should be the speed of the throw so that more t han two balls are in the the sky at any time (g = 9.8 m/s2)
[CPMT-2003]
[1] only with speed 19.6 m/s
[2] more than 19.6 m/s
[3] at least 9.8 m/s
[4] any speed less than 19.6 m/s
Q.63 If a ball is thrown vertically upwards with sped u, the distance covered during the last t seconds of its ascent is
[1] ut
[ 2]
1 2 gt 2
[3] ut −
1 2 gt 2
]
[4] u + gt t [CPMT-2003]
particle move moves s in a straight straight line line with retardation proportional proportional to its its displacem displacemen ent. t. Its loss of kinetic kinetic ene energy rgy for any any Q.64 A particle displacement x is proportional to
[AIEEE-2004]
[ 2] ex
[1] logex
[4] x2
[3] x
is released released from the top of a tower of heigh heightt h meters. It takes T seconds seconds to reach the ground. ground. What What is the Q.65 A ball is position of the ball at
[1]
[3]
17h 18 8h 9
T 3
second
met er from the ground
meter f rom the ground
[AIEEE-2004]
[2]
[4]
Q.66 The relation between time t and distance x is t = ax is -
[1] –2av3
[2] 2av2
2
7h 9 h 9
meter from the ground
meter from the ground
+ bx where a and b are constants. The acceleration [AIEEE-2005]
[3] –2abv2
[4] 2bv3
M otion in one dimensions dimensions
accelerates at the rate f through through a distance distance S then continue continues s at constant constant speed for Q.67 A car, starting from rest, accelerates time t and then decelerates at the rate
1
[1] S =
2
ft 2
[2] S =
1 4
f 2
to come to rest. If the total distance traversed is 15 S, then -
ft 2
[3] S = 2ft 2
[4] S =
1 6
ft 2 [AIEEE-2005]
particle is is movin moving g eastwards eastwards with a veloci velocity ty of 5 ms ms –1 . In I n 10 seconds the velocity changes to 5 ms –1 northwards. Q.68 A particle The average acceleration in this time is [AIEEE-2005]
[1] zero
[3]
1 2
ms
1
[2]
−
2
towards north-east
[4]
2
1 2
ms
ms
−
2
−
2
towards north-west
towards-north
bullet fired fired into into a fixed fixed target loses loses half half of its veloci velocity ty after penen penentarting tarting 3 cm. How How much further further it will pene penetrate trate Q.69 A bullet before befor e coming to rest assuming assuming that if faces fac es constant istance to motion [AIEEE-2005] [1] 1.5 cm
[ 2] 1.0 cm
[3] 3.0 cm
[4] 2.0 cm
parachutistt after bailin bailing g out out falls 50 m without without friction. friction. When parachute parachute opens, it decelerates decelerates at 2m/s 2. He Q.70 A parachutis reaches the ground with a speed of 3m/s. At what height, did he bail out [1] 293 m
[ 2] 111 m
[3] 91 m
[AIEEE-2005]
[4] 182 m
Q.71 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 v1 . The boy at A starts running simultaneously with velocity v and catches
the other boy in a time t, where t is [1] a / v 2
+
v 12
[2] a / ( v + v 1 )
[CPMT-2005]
[3]
a 2 /( v 2
vertically upward. upward. It has has a speed of Q.72 A ball is thrown vertically height. How high does the ball rise? Take g = 10 m/s 2 [1] 20 m
[ 2] 15 m
[3] 5 m
−
v 12 )
[4] a/(v a/(v – v1)
when it has has reached one one half half of its maximu maximum m [CPMT-2005] [4] 10 m
Q.73 What will be the a vs x graph for the following graph?
[1]
[2]
[IIT Scr. -2005]
[3]
[4]
M otion in one dimensions dimensions
particle located located at x = 0 at time t = 0, starts movin moving g along along the the positiv positive e x-direction x-direction with a velocity velocity 'v' 'v' that that varies as Q.74 A particle v = a x . The displacement of the particle varies with time as [ 2] t 1/2
[1] t
[AIEEE-2006]
[3] t 3
[4] t 2
runs at a constant constant speed on a crcular crcular track of radius radius 100m, 100m, taking taking 62.8 seconds seconds for every every circular circular lap. Q.75 A car runs the average velocity and average speed for each circular lap respectively [CPMT-2006] [1] 0, 10 m/ s
[ 2] 10 m/ s, 10 m/s
[3] 10 m/s , 0
[4] 0, 0
moves along along a straight straight line line OX. At a time t (in secon seconds) ds) the distance distance x (in metres) of the the particle from O Q.76 A particle moves 3 is given by x = 40 + 12t – t . How long would the particle travel before coming to rest. [CPMT-2006] [1] 40m
[ 2] 56m
[3] 16m
[4] 24m
Q.77 Two bodies, A(of mass 1kg) and B (of mass 3kg), are dropped from heights of 16m and 25m, respectively. The ratio of the time taken by them to reach the ground is [CPMT-2006]
[1] 12/5
[2] 5/ 12
[3] 4/5
ANSWER KEY Q us . Ans. Q us . Ans. Q us . Ans. Q us . Ans. Q us . Ans. Q us . Ans.
1 4 16 3 31 2 46 2 61 4 76 3
2 3 17 2 32 3 47 2 62 2 77 3
[4] 5/4
EXERCISE # 3 3 3 18 2 33 2 48 1 63 2
4 3 19 3 34 4 49 2 64 4
5 1 20 4 35 3 50 4 65 3
6 3 21 4 36 3 51 2 66 1
7 1 22 2 37 2 52 1 67 3
8 4 23 2 38 2 53 1 68 2
9 1 24 3 39 2 54 3 69 2
10 4 25 1 40 1 55 2 70 1
11 2 26 2 41 3 56 2 71 3
12 1 27 3 42 1 57 3 72 4
13 1 28 2 43 2 58 1 73 3
14 2 29 2 44 4 59 2 74 4
15 2 30 3 45 1 60 1 75 1
