Form 4 Chapter 2 Forces and Motion Mot ion 2.1 Linear Motion 1. Lin Linear ear moti motion on is is motion motion in a strai straight ght lin line. e. 2. The stu study dy of of the the motio motion n of an obje object ct without considering the forces acting on it is called kinematics.
3. Und Under er line linear ar moti motion, on, we stu study dy the a. di dist stan ance ce and and di disp spla lacem cemen entt b. speed and velocity c. cc cceler elerati ation on and and the relati relations onship hip betw between een them. them. Distance Definition! The distance traveled by an object object is the total length that is traveled by that object. SI unit! meter "m# Quantity! $calar
Displacement Definition! %isplacement of an object from a point of reference, & is the shortest distance of the object from point & in a specific direction. SI unit meter "m# Quantity! Vector
!"ample!
The distance of point ' from the origin & is 1((m. The distance of point from the origin & is also 1((m. The displacement of of point # from the origin $ is %1((m. The displacement of of point & from the origin $ is )1((m. The * and + sign show the direction of the displacement.
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!"ample!
li go to wor by motorcycle everyday as shown in the diagram above. The distance that li travels from his house to the factory is 2((m. The displacement of of li from his house after arriving at the factory is 12( m.
Speed 1. $pee $peed d is is defi define ned d as the the rate of change in distance . -t is a measure of how fast the distance change in a movement.
2. $peed is a scalar 'uantity . 3. The The $$- uni unitt of of spe speed ed is m(s "metre per second#
!'uation of Speed
)elocity 1. elocity locity is define defined d as as the the rate of change in displacement . -t is the measure of how fast the displacement change of a moving object.
2. eloci locity ty is a *ector 'uantity . 3. The unit unit of of velocit velocity y is m/s m/s "metre "metre per per second# second#
!'uation of *elocity
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&cceleration 1. cceleration is defined as the rate of change of velocity . -t is a measure of how fast the *elocity change.
2. cceleration is a *ector 0uantity. 3. The unit of acceleration is ms+2. . n object moving with a *elocity that is decreasing is said to be eperiencing deceleration.
Equation of acceleration
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Example: car travels from a stationary position and reach a velocity of 3 ms )1 in 4 seconds. 5hat is the acceleration of the car6 &nswer!
-nitial velocity , u = 0 7inal velocity , * = 36 ms-1 Time taen, t = 8s Acceleration, a = ?
a8
v −u t
8
36 −0 8
= 4., ms+2
!'uation of -niform &cceleration 9ost of the motion problems can be solved by the following e0uations. Therefore, mae sure that you memorise all of them.
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ow we know when to use the e'uation/
The e0uations are used when the motion is uniform acceleration.
Motion with -niform &cceleration !"ample 0! n object accelerates from stationary with the acceleration of ms)2. 5hat is the velocity of the object after :s6 &nswer!
-t;s advisable to list down all the information that we have. -nitial velocity, u 1 "'ecause the motion start from stationary# cceleration, a 1 4 ms+2 Time taen, t 1 3s 7inal velocity, * 1 / The displacement, s, is not involved, hence we select the e0uation * 1 u % at to solve the problem. * 1 u %at * 8 "(# * "# ":#<
7inal velocity, * 8 25ms+0
!"ample 2 car is moving with velocity =ms )1 reaches a velocity of 2=ms )1 in =s. 5hat is the acceleration of the car6 &nswer! -t;s advisable to list down all the information that we have.
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-nitial velocity, u 8 =ms)1 7inal velocity, * 8 2=ms)1 Time taen, t 8 =s cceleration, a 8 6
!"ample 6 cyclist riding at a speed of ( ms )1 braed with uniform acceleration and stopped in (m. >ow long did he tae to stop6
&nswer! -nitial velocity, u 8 ( ms )1 7inal velocity, v 8 ( "'ecause the cyclist stop# %isplacement, s 8 (m Time taen, t 8 6
!"ample 4 car is accelerated at ms)2 from an initial velocity of = ms )1 for 1( seconds. 5hat is the distance travelled by the car6 &nswer!
cceleration, a 8 ms)2 -nitial velocity, u 8 = Time taen, t 8 1(s %isplacement, s 8 6
!"ample , car accelerates from ms)1 reaches a velocity of 24 ms )1 after travelling for m. 5hat is the acceleration of the car6 &nswer! -nitial velocity, u 8 ms )1 7inal velocity, v 8 24 ms )1 %isplacement, s 8 m cceleration, a 8 6
!"ample 7 car begins to move from rest. The velocity of the car increases at a rate of ms )2. 7ind the distance travelled by the car after 12 second. &nswer!
-nitial velocity, u 8 ( "'ecause the begins to move from rest# 6
cceleration, a 8 ms)2 "?ate of increment 8 cceleration# Time taen, t 8 12s %isplacement, s 8 6
!"ample 3
body is accelerated uniformly from rest and in the first .( s of its motion it travels 3( m. 7ind i. ii. iii.
the average speed for this period of s, the speed at the end of this period, the acceleration.
&nswer!
-nitial velocity, u 8 ( "'ecause the motion start from rest# Time taen, t 8 .(s %isplacement, s 8 3(m 7inal velocity, v 8 6 cceleration, a 8 6 Total Distancetravelled
i. verage speed 8
Total time taken
ii. the speed at the end of this period
30 m
=
= ,. ms+0
6s
iii. the acceleration.
1
s1
2
1
8u % *9 t
s 1 ut %
1
3( 8
2
2
at2
1
"( * v#
v 8 1( ms+0
3( 8 ( *
2
a "#2
14a 8 3( a 1 0.773 ms +2
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Challenging Question 0! car starts from rest and accelerates at a constant acceleration of 3 ms)2 for 1( seconds. The car then travels at a constant velocity for = seconds. The braes are then applied and the car stops in = seconds. 5hat is the total distance travelled by the car6
Challenging Question 2! li starts driving his car from home with a constant acceleration and reaches a velocity of 3( m/s in .( seconds. 7ind a.
The acceleration of li;s car.
b.
The displacement of li;s car =.( seconds after it started moving.
c.
The displacement of li;s car in the fifth second..
d.
elocity of li;s car at time t 8 .( seconds6
e.
elocity of li;s car after moving 3(.( meters from the starting point.
2.0 :icker + :imer
1. ticer ) timer consists of an electrical vibrator which vibrates =( times per second. 2. This enables it to mae =( dots per second on a ticer)tape being pulled through it. 3. The time interval between two adjacent dots on the ticer)tape is called one tick . . &ne tic is e0ual to 1/=( s or (.(2 s.
Example: 7ind the number of ticks and the time interval between the first dot and the last dot on each of the ticer tapes below. The frequency of the ticer timer is e0ual to 50Hz .
a.
&nswer! @umber of tics 8 0,
8
Time interval 8 1= (.(2s 8 .6s
b.
&nswer! @umber of tics 8 ,
Time interval 8 = (.(2s 8 .0s
c.
&nswer! @umber of tics 8 5
Time interval 8 4 (.(2s 8 .07s
The distance between dots on a ticker tape 1. The distance between two adjacent dots on a ticer)tape represents the displacement of the object in a tick 0!0" s#! 2. -f the object moves quickly, the dots are far apart . -f the object moves slowly, the dots are close to each other .
$nalysing %icker %ape
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Finding )elocity from :icker :ape &inding Velocity elocity of a motion can be determined by using ticer tape through the following e0uation!
Caution;
t is time taen from the first dot to the last dot of the distance measured. !"ample!
%iagram above shows a strip of ticer tape that was pulled through a ticer tape timer that vibrated at =( times a second. 5hat is the 10
a. Time taen from the first dot to the last dot6 b. elocity of the object that is represented by the ticer tape6
&nswer! a. There are 1= tics from the first dot to the last dot, hence Time taen 8 1= A (.(2s 8 (.3s b. %istance travelled 8 1=cm 15 cm
elocity 8
0.3 s
8 ,
cms
−1
Caution;
t is time taen from the initial velocity to the final velocity.
!"ample!
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The ticer)tape in figure above was produced by a toy car moving up a tilted runway. -f the ticer) tape timer produced =( tics per second, find the deceleration of the toy car.
&nswer! -nitial velocity, 3 cm
u =
0.02 s
=150
−1
cms
7inal velocity, 0.5 cm
v=
0.02 s
= 25
−1
cms
Time taen for the velocity change, t 8 ")1# tics 8 = tics t 8 = A (.(2s 8 (.1s
a =
v −u t
=
25 −150 0.1
= 1250
!eceleration = 1250
cms
−1
−1
cms
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2.2 &nalysing Motion
2.2 &nalysing Motion
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Velocity'time (raphs
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!"ample
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Displacement'time (raph
Velocity'time (raphs
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)omparison between the displacement'time graph and velocity'time graph*
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+on'uniform motion
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