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Kinematics

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Dynam deals with the motion of bodies with
ics
reference to the forces that act on the system.
Kinem atics deals with the motion of bodies
without reference to the forces that act on the
system.
Two types of motion will be studied:
1. One dimensional motion
- rectilinear motion
2. Two dimensional motion
- projectile motion

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1. Definition of terms
[I] Displacement s
Displacem is the distance travelled
ent
along a specified direction.
B
Body travels along
curved path from A
to B. A
It is a vector quantity.
SI unit: m etre, m

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[II] Speed v
Speed is the rate of change of
distance.
It is a scalar quantity.
SI unit: m s-1
average speed
< v > = total distance covered
total time taken
A body that travels equal distances in equal
intervals of time is said to be moving with
c o ns ta nt or unifo rm speed.

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Estimates of speeds (in m s-1)
walking 1.5
sprinter 10
Speed limit 25 [ie. 90 km h-1]
Jet plane 250
Sound (in air) 330
Light (in vacuum) 3.00 × 108

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[III] Velocity v
Velocity is the rate of change of
displacem ent.
It is a vector quantity.
SI unit: m s-1 ds
v=
dt
average velocity
rate of
total displaceme nt change
<v > =
total time taken

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A body which travels equal distances in
the same direction in equal intervals of
time is said to be moving with c o ns ta nt
or unifo rm velocity.
< speed > may not always be
equal to < velocity >

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Example 1:
(a) total distance = 5.0 + 5.0 = 10.0 km
(b) displacement = 5.0 2 + 5.0 2
N
= 7.1 km 5.0 km
θ
5 .0
tan θ = = 1 .0 5.0 km
5 .0
⇒ θ = 45o
Displacement is 7.1 km at a bearing of 135 o
or S45oE.

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10.0
(c) <speed> =
1 .0
= 10 km h-1
7 .1
(d) <velocity> =
1.0
= 7.1 km h-1
at a bearing of 135o

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[IV] Acceleration a
Acceleration is the rate of change of
velocity.
It is a vector q ua ntity . dv
a=
SI unit: m s-2 dt
A change in velocity can be caused by:
(i) a change in its magnitude only,
(ii) a change in its direction only, or
(iii) a change in both its magnitude and
direction.

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A body which travels with equal increase
in speed in the same direction in equal
intervals of time is said to be moving
with c o ns ta nt or unifo rm acceleration.
acceleration = 0 ⇒ constant velocity
But when velocity = 0 at one instant,
acceleration need not be zero. (Think
of a situation where this can happen.)

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Retardation or deceleration
describes a situation when magnitude of
velocity decreases with time
i.e. body is slowing down.
This occurs when acceleration and velocity act
in opposite directions.
In the next slide, observe the directions of the
velocity and acceleration when a body travels
faster and when it slows down.

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Free fall
K A body is said to be in fre e fa ll if the only
i force acting on it is the gravitational force
e due to the Earth.
m
The downward acceleration of such a body
a
is known as a c c e le ra tio n d ue to g ra vity .
t g = 9.81 m s-2
c (assumed to be constant near Earth’s surface)
s
True free fall only occurs in vacuum.
All bodies falling freely will have this constant
acceleration regardless of their masses.

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2 Graphical Representation of Motion
K
2.1 Displacement-time graph
i
n displacement , s average velocity
between O and A = S1
e t1
s1
m A
(gradient of the line
a passing through O & A)
t
s
time, t
O t1

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displacement , s
slope at A =
s1 A ds instantaneous
velocity at A
ds
dt =
dt
time, t
O t1

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body is stationary
x
or velocity is zero
A B x decreases at a constant
rate ⇒ body is moving
back towards O. Velocity
is negative, uniform and
greater in magnitude than
t
that of OA.
0 x increases at a constant rate
C
⇒ body is moving with uniform velocity
x
O A

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Examples of displacement-time graphs
(a) s
t
uniform velocity (constant gradient)

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Examples of displacement-time graphs
(b) s
curve 1
t
Curve 1: increasing velocity
(gradient increasing)

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Examples of displacement-time graphs
(b) s
curve 2
t
Curve 2: decreasing velocity
(gradient decreasing)