This chapter discusses kinematics of linear motion, including: 1) It defines kinematics as the study of motion without considering forces, and describes linear and projectile motion. 2) It introduces key concepts such as displacement, speed, velocity, acceleration and their relationships. Equations for these quantities under constant and uniformly accelerated motion are provided. 3) It describes motion under constant acceleration due to gravity, known as freely falling bodies, and provides the relevant equations.

1. 1
CHAPTER 2:
Kinematics of Linear Motion

2. 2
2.0 Kinematics of Linear motion
 is defined as the studies of motion of an objects without considering
the effects that produce the motion.
 There are two types of motion:
 Linear or straight line motion (1-D)
 with constant (uniform) velocity
 with constant (uniform) acceleration, e.g. free fall motion
 Projectile motion (2-D)
 x-component (horizontal)
 y-component (vertical)

3. 3
Learning Outcomes :
At the end of this chapter, students should be able to:
• Define and distinguish between
 Distance and displacement
 Speed and velocity
 Instantaneous velocity, average velocity and uniform velocity
 Instantaneous acceleration, average acceleration and uniform acceleration,
• Sketch graphs of displacement-time, velocity-time and acceleration-time.
• Determine the distance travelled, displacement, velocity and acceleration from
appropriate graphs.
2.1 Linear Motion

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2.1. Linear motion (1-D)
2.1.1. Distance, d
• scalar quantity.
• is defined as the length of actual path between two points.
• For example :
– The length of the path from P to Q is 25 cm.
P
Q

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 vector quantity.
 is defined as the distance between initial point and final point in a straight line.
 The S.I. unit of displacement is metre (m).
Example 2.1 :
An object P moves 30 m to the east after that 15 m to the south
and finally moves 40 m to west. Determine the displacement of P
relative to the original position.
Solution :
2.1.2 Displacement,
N
E
W
S
O
P


30 m
15 m
10 m 30 m

6. 6
The magnitude of the displacement is given by
and its direction is
2.1.3 Average Speed, v
 is defined as the rate of total distance travelled.
 scalar quantity.
 Equation:
interval
time
travelled
distance
total
speed
Average 
Δt
d
v



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interval
time
nt
displaceme
of
change

av
v
1
2
1
2
av
t
t
s
s
v



 is a vector quantity.
 The S.I. unit for velocity is m s-1.
Average velocity, vav
 is defined as the rate of change of displacement.
 Equation:
 Its direction is in the same direction of the change in displacement.
2.1.4 Velocity,
Δt
Δs
vav 

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constant

dt
ds
t
s
0
t
v





limit
Instantaneous velocity, v
 is defined as the rate of change of displacement at the
particular time, t
 Equation:
 An object moves in a uniform velocity when the magnitude and
direction of the velocity remain unchanged.
and the instantaneous velocity equals to the average velocity at
any time.
dt
ds
v 

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 Therefore
Q
s
t
0
s1
t1
The gradient of the tangent to the curve at point Q
= the instantaneous velocity at time, t = t1
Gradient of s-t graph = velocity

10. 10
interval
time
velocity
of
change

av
a
 vector quantity.
 The S.I. unit for acceleration is m s-2.
Average acceleration, aav
 is defined as the rate of change of velocity.
 Equation:
 Its direction is in the same direction of change in velocity.
 The acceleration of an object is uniform when the magnitude of velocity changes at a
constant rate and along fixed direction.
2.1.5 Acceleration,
1
2
1
2
av
t
t
v
v
a



Δt
Δv
aav 

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constant

dt
dv
t
v
0
t
a





limit
Instantaneous acceleration, a
 is defined as the rate of change of velocity at the particular time,t.
 Equation:
 An object moves in a uniform acceleration when
and the instantaneous acceleration equals to the average acceleration at
any time.
2
2
dt
s
d
dt
dv
a 


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 Therefore
v
t
Q
0
v1
t1
The gradient of the tangent to the curve at point Q
= the instantaneous acceleration at time, t = t1
Gradient of v-t graph = acceleration

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Deceleration, a
 is a negative acceleration.
 The object is slowing down meaning the speed of the object
decreases with time.
Gradient of v-t graph at point C = Negative acceleration
v
t
0
C

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Displacement against time graph (s-t)
2.1.6 Graphical methods
s
t
0
s
t
0
(a) Uniform velocity (b) The velocity increases with time
Gradient = constant
Gradient increases
with time
(c)
s
t
0
Q
R
P
The direction of
velocity is changing.
Gradient at point R is negative.
Gradient at point Q is zero.
The velocity is zero.

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 From the equation of instantaneous velocity,
Therefore

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Velocity versus time graph (v-t)
 The gradient at point A is positive – a > 0(speeding up)
 The gradient at point B is zero – a= 0
 The gradient at point C is negative – a < 0(slowing down)
t1 t2
v
t
0
(a) t2
t1
v
t
0
(b)
t1 t2
v
t
0
(c)
Uniform velocity
Uniform
acceleration
Area under the v-t graph = displacement
B
C
A

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Learning Outcome :
At the end of this chapter, students should be able to:
• Derive and apply equations of motion with uniform
acceleration:
2.2 Uniformly accelerated motion
at
u
v 

2
2
1
at
ut
s 

as
u
v 2
2
2



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2.2. Uniformly accelerated motion
From the definition of average acceleration,
uniform (constant) acceleration is given by
wherev : final velocity
u : initial velocity
a : uniform (constant) acceleration
t : time
at
u
v 
 (1)
t
u
v
a



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 From equation (1), the velocity-time graph is shown in Figure 2.4 :
 From the graph,
The displacement after time, s = shaded area under the
graph
= the area of trapezium
 Hence,
velocity
0
v
u
time
t
Figure 2.4
 t
v
u
2
1
s 
 (2)

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 By substituting eq. (1) into eq. (2) thus
 From eq. (1),
 From eq. (2),
 
 t
at
u
u
s 


2
1
(3)
2
2
1
at
ut
s 

  at
u
v 

 
t
s
u
v
2


multiply
    
at
t
s
u
v
u
v 








2
as
u
v 2
2
2

 (4)

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 Notes:
 equations (1) – (4) can be used if the motion in a straight
line with constant acceleration.
 For a body moving at constant velocity, ( a = 0) the
equations (1) and (4) become
Therefore the equations (2) and (3) can be written as
u
v 
vt
s  constant velocity

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Learning Outcome :
At the end of this chapter, students should be able to:
• Describe and use equations for freely falling bodies.
– For upward and downward motion, use
a = g = 9.81 m s2
2.3 Freely falling bodies

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2.3 Freely falling bodies
• is defined as the vertical motion of a body at constant acceleration, g
under gravitational field without air resistance.
• In the earth’s gravitational field, the constant acceleration
– known as acceleration due to gravity or free-fall acceleration or gravitational
acceleration.
– the value is g = 9.81 m s2
– the direction is towards the centre of the earth (downward).
• Note:
– In solving any problem involves freely falling bodies or free fall motion, the
assumption made is ignore the air resistance.

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 Sign convention:
 Table 2.1 shows the equations of linear motion and freely falling
bodies.
Table 2.1
Linear motion Freely falling bodies
gt
u
v y
y 

y
y
y gs
u
v 2
2
2


2
2
1
gt
t
u
s y
y 

+
- +
-
From the sign convention
thus,

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THE END…
Next Chapter…
CHAPTER 3 :
Newton's Law & Its application