SP015 Lecture Notes Ch 02

SP015

CHAPTER 2:

KINEMATICS OF LINEAR
MOTION

2.1 Linear Motion

Learning Outcomes:

2.1 a) Define

i. instantaneous velocity , average velocity &
uniform velocity

ii. instantaneous acceleration , average
acceleration & uniform acceleration.

b) Discuss the physical meaning of displacement-time,
velocity-time and acceleration-time graphs.

Kinematics of linear motion

 is defined as the studies of motion of an object in a straight line without

considering the effects that produce the motion and what causes the motion

Two types of motion:

Linear or straight line motion (1-D) Projectile motion (2-D)

- with constant (uniform) - x-component
velocity (horizontal)

- with constant (uniform) acceleration, - y-component
e.g. Free fall (vertical)

2.1 (a) Define instantaneous velocity , average velocity & uniform velocity, instantaneous
acceleration , average acceleration & uniform acceleration.

Velocity, v Acceleration, a

• rate of change of • rate of change of velocity.
displacement. • S.I. unit : m s-2; vector

• S.I. unit : m s-1; vector quantity.
quantity.

Instantaneous
Velocity

velocity at a particular
instant of time along the

path of motion or the
instantaneous rate of
change of displacement.

Average
Velocity

change in velocity
divided by the time taken

to make the change.

Uniform
Velocity

magnitude of
displacement changes at a

constant rate and along
fixed direction

Type Definition Equation

Instantaneous acceleration at a particular
Acceleration, instant of time or the
instantaneous rate of change of
velocity.

Average change in velocity divided by
Acceleration, aav the time taken to make the
change.

Uniform magnitude of velocity changes
Acceleration, at a constant rate and along
fixed direction.

2.1 (b) Discuss the physical meaning of displacement-time (s-t),
velocity-time (v-t) and acceleration-time (a-t) graphs.

s

0t

Gradient of displacement-time graph = Velocity
Area under the velocity-time graph = Displacement

Displacement-time (s-t) Graph

 Gradient of displacement-time graph = Velocity

ss s

0t 0t 0t

Displacement = increases Displacement = increases Displacement = constant
Velocity = constant exponentially Velocity = zero
Velocity = increases

Velocity -time (v-t) Graph

 Gradient of velocity-time graph = Acceleration
 Area under the velocity-time graph = Displacement

vv v

0 t0 t 0 t

Velocity = increases Velocity = increases Velocity = constant
Acceleration = constant exponentially Acceleration = zero
Acceleration = increases

Acceleration -time (a-t) Graph
 Area under the acceleration-time graph = Velocity

aa

0t 0t
Acceleration = increases Acceleration = constant

s-t v-t a-t

va

0 t0 t
va

0 t0 t

2.0 KINEMATICS OF LINEAR MOTION
2.3 Projectile motion

Learning outcomes:
Describe projectile motion launched at

an angle 

at angle  = 0

 = 90 (free fall)

Example of projectile motion

Projectile A motion where object
motion? travels at a uniform
velocity in the
two
horizontal direction; at dimensional
the same time
undergoing motion

acceleration in the
downward direction
under the influence of

gravity.

A projectile
motion

consists of
two

components

free fall Assumptions of
acceleration g projectile
is constant and motion

is always
directed
downward

Neglect
air

resistance

Understanding Projectile Motion

Kinematic equations for projectile motion in x and y
components

Kinematic equations for projectile motion in x and y
components

Equation of linear x-component y-component
motion (horizontal) (vertical)

Initial velocity

1st CASE : Projectile motion launched at any angle

Angle launched on level ground Angle launched from a certain
height

2nd CASE : Projectile motion launched at  = 0
(zero launch angle)

If an object is projected
horizontally, there should be no
angle of projection, so  = 0

3rd CASE : Free falling body (object launched at  = 90)

is defined as the vertical motion of a body at constant acceleration, g under
gravitational field without air resistance / linear vertical motion under the sole
influence of gravity
In the earth’s gravitational field, the constant acceleration :

known as acceleration due to gravity or gravitational acceleration

the direction is towards the centre of the earth (downward with an acceleration
a = – g)

the value is g = 9.81 m s-2
NOTE!
In solving any problem involves free fall motion, the
assumption made is ignore the air resistance

g (vector quantity) is given a minus (–) sign
indicating that it is always directed
downward.

Replace a with – g into kinematics equation

Value of s, u, v may be (+) or (–) depending
on the direction of motion

Equation of linear motion & free fall motion

Equation of linear motion Free falling body

g (vector quantity) is given a minus (–) sign
indicating that it is always directed
downward.

Replace a with – g into kinematics equation

Value of s, u, v may be (+) or (–) depending
on the direction of motion

Sign convention

An object is An object is An object is
released from thrown thrown
upward
rest downward
+u
Initial velocity, u u=0 -u
Final velocity, v v=0
Acceleration, a -v -v
Displacement, s a = -g
a = -g a = -g
s = +h
s = -h s = -h