2023 O SCIPHY 02 Kinematics Teaching Slides Lesson

1

Chapter 2
Kinematics

Discover Physics for
GCE ’O’ Level Science and
Normal (A) Level Science

2

Recap: scalar vs vectors

Learning Outcome(s)
• State what is meant by scalar and vector quantities and give common examples

of each.

3

1.4 What Are Scalars and Vectors?

• Scalar quantities are physical quantities that have only magnitude.
• Vector quantities are physical quantities that have both magnitude and

direction.

Textbook
Page 12

Only magnitude
Both magnitude and

direction

4

Distance and Displacement
Let’s look at the following to understand the meanings of distance and
displacement.

1.4 What Are Scalars and Vectors?

Textbook
Page 12

Distance
• Total length covered by moving
object, along the path taken
• Direction of motion does not
matter
• SI unit: metre (m)

Displacement
• Straight-line distance covered by
moving object, regardless of path
taken
• Direction needs to be specified
• SI unit: metre (m)

5

14 km (blue
path)

0 km (back at
A)

Distance and Displacement
Let’s look at the following to understand the meanings of distance and
displacement.

20 km (green
path)

1.4 What Are Scalars and Vectors?

Question:
• What if the object

moves back to A
along the same path?
(i.e. A 🡪 B 🡪 A)

Textbook
Page 12

6

1.4 What Are Scalars and Vectors?

Distance and Displacement
Let’s look at the following to understand the meanings of distance and
displacement.

(a)
What is the distance travelled from A to F?

(b)
What is the displacement from A to F?

7

1.4 What Are Scalars and Vectors?

Distance and Displacement
Let’s look at the following to understand the meanings of distance and
displacement.

(a)
What is the distance travelled from A to F?

Ans: 21 m

(b)
What is the displacement from A to F?

Ans: – 3 m

8

Questions:

• Is it possible to have a negative distance or displacement?

• If yes, what is the possible reason?

1.4 What Are Scalars and Vectors?

9

Positive and Negative Displacement

1.4 What Are Scalars and Vectors?

A

B

− 5 km

5 km

+−

• For an objectmoving in a straight line, assign one direction from the reference point as positive.

• The opposite direction is then negative.

• Positive−negative directions are assigned for convenience (sign conventions).

− 2 km

C

Distance of car = 12 km

Displacement of car = − 2 km (or 2 km due west of A)

10

Positive and Negative Displacement

1.4 What Are Scalars and Vectors?

A car travels 8 km to the right.

Then, the car makes a U-turn and travels a further 6 km to the left.

What is the distance covered by the car and what is its displacement at the end of the journey?

11

Positive and Negative Displacement

1.4 What Are Scalars and Vectors?

A car travels 8 km to the right.

Then, the car makes a U-turn and travels a further 6 km to the left.

What is the distance covered by the car and what is its displacement at the end of the journey?

Solution

Distance covered = 8 + 6 = 14 km

Displacement = 8 – 6 = 2 km to the right of the starting point

12

1.4 What Are Scalars and Vectors?

Speed and Velocity
Let’s compare the differences between speed and velocity.

As velocity is a vector quantity, it is speed in a specified direction.

Speed

Velocity

• Defined as the distance moved

per unit time

• Defined as the rate of change of

displacement

• A scalar quantity

• A vector quantity

• SI unit is metre per second (m/s)

Textbook
Page 13

13

Lesson 2.1A
(double period)

14

Activate Prior Knowledge

Launch Quiz 2.1

Let’s play a quiz on your personal learning device to test your prior knowledge from
the past lessons!

15

Chapter 2 Kinematics

• 2.1 What Are Speed, Velocity and Acceleration?
• 2.2 How Do We Analyse Motion Graphically?
• 2.3 What Is Acceleration of Free Fall?

16

2.1 What Are Speed, Velocity and Acceleration?

Learning Outcome(s)
• State what is meant by speed and velocity.
• Calculate average speed using distance travelled / time taken.
• State what is meant by uniform acceleration and calculate the value of

acceleration using change in velocity / time taken.

• Interpret given examples of non-uniform acceleration.

17

Capture Interest

18

National Day Parade Flypast

• Have you watched the flypast by the Republic of Singapore Air Force aerobatics

team before?

• How can we describe and analyse the motion of the jets as they fly at varying

speeds in curved and straight lines?

Textbook
Page 17

19

Construct
Understanding

20

2.1 What Are Speed, Velocity and Acceleration?

• In the 2016 Rio Olympics, Usain Bolt, clocked an amazing time of 9.81 seconds as

he crossed the finishing line and became the winner of the men’s 100-metre final.

• With this win, he became the first person in history to win the 100-metre race

three times in three consecutive Olympics.

Textbook
Page 18

Question:
If Usain Bolt were to race against a
cheetah in a 100-metre sprint, who would
be the winner?

21

•

2.1 What Are Speed, Velocity and Acceleration?

Textbook
Page 18

22

2.1 What Are Speed, Velocity and Acceleration?

•

Textbook
Page 19

Average speed assumes that
each athlete ran at the same
speed throughout the entire
distance.

In reality, the athletes did not
run at the same speed
throughout their races.

23

2.1 What Are Speed, Velocity and Acceleration?

d

v

t

Worked Example 1

Tom travels 105 km in 2.5 hours before stopping for a half-hour lunch. He
then continues another 55 km for an hour. What was the average speed of
his journey in
(a) km/h?
(b) m/s?

24

2.1 What Are Speed, Velocity and Acceleration?

d

v

t

Worked Example 1

Tom travels 105 km in 2.5 hours before stopping for a half-hour lunch. He
then continues another 55 km for an hour. What was the average speed of
his journey in
(a) km/h?
(b) m/s?

1 km = 1000 m

1 h = 60 min
= 60 x 60 s
= 3600 s

25

Worked Example 2

Convert 54 km/h to m/s

Convert 30 m/s to km/h

2.1 What Are Speed, Velocity and Acceleration?

26

Worked Example 2

Convert 54 km/h to m/s

Convert 30 m/s to km/h

2.1 What Are Speed, Velocity and Acceleration?

27

Let’s Understand

Refer to Textbook pg 19 for

Worked Example 2A

28

2.1 What Are Speed, Velocity and Acceleration?

Instantaneous Speed
• Instantaneous speed is the speed of an object at a particular instant.
• SI unit for instantaneous speed is metre per second (m/s).

Question:
• Do you know what does a speedometer show?

Textbook
Page 19

29

2.1 What Are Speed, Velocity and Acceleration?

Uniform Speed
• Uniform (constant) speed is when the change in the distance travelled by an

object per unit time is the same.

• SI unit for uniform speed is metre per second (m/s).
• From Table 2.2 and Figure 2.4, it is shown that for an object moving with a

uniform speed in 10 m/s, the distance travelled per unit time is 10 m.

Textbook
Page 20

30

2.1 What Are Speed, Velocity and Acceleration?

Worked Example 3

A bike travels at a constant speed of 10.0 m/s. It takes 2000 s to travel from
Jurong to East Coast. Determine the distance between the two locations.

d

v

t

31

2.1 What Are Speed, Velocity and Acceleration?

Worked Example 3

A bike travels at a constant speed of 10.0 m/s. It takes 2000 s to travel from
Jurong to East Coast. Determine the distance between the two locations.

Solution

Speed v = 10 m/s

Time t = 2000 s

Distance d = v x t

= 10 m/s x 2000 s

= 20 000 m or 20 km

d

v

t

32

Let’s Understand

Refer to Textbook pg 20 for

Worked Example 2B

33

2.1 What Are Speed, Velocity and Acceleration?

Recall: Differences between Distance and Displacement

Textbook
Page 21

34

Let’s Understand

Refer to Textbook pg 21 for

Worked Example 2C

35

2.1 What Are Speed, Velocity and Acceleration?

Textbook
Page 22

d

v

t

The “triangle” method
can help you to recall
the relationship between
velocity v, displacement d
and time t.

•

36

Velocity

Speed

Vector Quantity

(both magnitude and direction)

Scalar Quantity

(only magnitude, no direction)

If ‘right’ is taken as positive:

2.1 What Are Speed, Velocity and Acceleration?

10 m/s towards the right

10 m/s towards the left

OR – 10 m/s

10 m/s

Negative sign indicates

the direction!

37

Worked Example 1 (Part 1)

A car takes half an hour to travel 7 km from A to B. What is its

(a)

average speed in km/h?

(b)

average velocity in km/h?

2.1 What Are Speed, Velocity and Acceleration?

38

Worked Example 1 (Part 1)

A car takes half an hour to travel 7 km from A to B. What is its

(a)

average speed in km/h?

(b)

average velocity in km/h?

2.1 What Are Speed, Velocity and Acceleration?

39

Worked Example 1 (Part 2)

The car takes another half an hour to move back to A along the same path. What is its

(a)

new average speed in km/h?

(b)

new average velocity in km/h?

2.1 What Are Speed, Velocity and Acceleration?

40

Worked Example 1 (Part 2)

The car takes another half an hour to move back to A along the same path. What is its

(a)

new average speed in km/h?

(b)

new average velocity in km/h?

2.1 What Are Speed, Velocity and Acceleration?

41

Worked Example 1 (Part 3)

The car takes another 15 minutes to reach point C. What is its average velocity?

2.1 What Are Speed, Velocity and Acceleration?

42

Worked Example 1 (Part 3)

The car takes another 15 minutes to reach point C. What is its average velocity?

2.1 What Are Speed, Velocity and Acceleration?

Can velocity
be negative?

Can speed be

negative?

43

Worked Example 2

A truck makes a delivery trip from town A to town B in 15 minutes, and then from town B to
town C in 45 minutes. The distances between the towns are shown on the map. Determine

a)

the average speed and

b)

the average velocity for the entire journey (from towns A to C).

2.1 What Are Speed, Velocity and Acceleration?

44

Worked Example 2

A truck makes a delivery trip from town A to town B in 15 minutes, and then from town B to
town C in 45 minutes. The distances between the towns are shown on the map. Determine

a)

the average speed and

b)

the average velocity for the entire journey (from towns A to C).

2.1 What Are Speed, Velocity and Acceleration?

45

Let’s Understand

Refer to Textbook pg 22 &
23 for Worked Example 2D

& 2E

46

2.1 What Are Speed, Velocity and Acceleration?

Acceleration
• An object accelerates when its velocity changes.
• An object undergoes acceleration when
- its speed or direction changes; or
- when both its speed and direction change.

Textbook
Page 23

47

2.1 What Are Speed, Velocity and Acceleration?

•

Textbook
Page 23

48

2.1 What Are Speed, Velocity and Acceleration?

Textbook
Page 22

O
R

Change in
velocity

(acceleration)

Velocity
increases

(accelerating)

Positive

acceleration

Velocity
decreases

(decelerating)

Negative

acceleration

Retardation

49

Summary of Lesson 2.1A

•

50

Lesson 2.1B
(double period)

51

2.1 What Are Speed, Velocity and Acceleration?

Uniform Acceleration
• An object undergoes uniform (constant) acceleration when the change in the velocity

of the object per unit time is the same.

• When the velocity of an object is increasing by 20 m/s every second, the acceleration

is 20 m/s2.

• When the velocity is decreasing by 20 m/s every second, the acceleration is –20 m/s2

or the deceleration is 20 m/s2.

Textbook
Page 24

Velocity increases /

decreases at a
constant rate

52

2.1 What Are Speed, Velocity and Acceleration?

Uniform Acceleration
• Note that when an object is travelling at uniform acceleration, the

increase in the distance travelled per unit time is of a different
magnitude.

Textbook
Page 24

53

2.1 What Are Speed, Velocity and Acceleration?

•

Textbook
Page 24

54

Worked Example 1

The velocity of a car changes from 15 m/s to 10 m/s in 1.2 s. Determine its acceleration.

2.1 What Are Speed, Velocity and Acceleration?

Should the acceleration of the

car be positive or negative?

55

Worked Example 1

The velocity of a car changes from 15 m/s to 10 m/s in 1.2 s. Determine its acceleration.

2.1 What Are Speed, Velocity and Acceleration?

Should the acceleration of the

car be positive or negative?

56

Worked Example 2

A stationary truck accelerates with an acceleration of 1 m/s2 for 15 seconds. Determine the
final velocity.

2.1 What Are Speed, Velocity and Acceleration?

57

Worked Example 2

A stationary truck accelerates with an acceleration of 1 m/s2 for 15 seconds. Determine the
final velocity.

2.1 What Are Speed, Velocity and Acceleration?

Solution

Given information:

Initial velocity u = 0 m/s

Acceleration a = 1 m/s2

Time taken t = 15 s

58

Worked Example 3

A bus starts from rest and achieves a velocity of 20 m/s in 10 s while moving to the west
from a starting point O. Calculate its acceleration.

2.1 What Are Speed, Velocity and Acceleration?

v = 20 m/s

u = 0 m/s

59

Worked Example 3

A bus starts from rest and achieves a velocity of 20 m/s in 10 s while moving to the west
from a starting point O. Calculate its acceleration.

2.1 What Are Speed, Velocity and Acceleration?

Solution

Given information:

Initial velocity u = 0 m/s

Initial velocity v = 20 m/s

Time taken t = 10 s

v = 20 m/s

u = 0 m/s

60

Worked Example 4

A car travelling at 30 m/s comes to a stop in 5 s. Calculate its acceleration.

2.1 What Are Speed, Velocity and Acceleration?

Final velocity
v = 0 m/s

Initial velocity
u = 30 m/s

61

Worked Example 4

A car travelling at 30 m/s comes to a stop in 5 s. Calculate its acceleration.

2.1 What Are Speed, Velocity and Acceleration?

Solution

Given information:

Initial velocity u = 30 m/s

Initial velocity v = 0 m/s

Time taken t = 5 s

Final velocity
v = 0 m/s

Initial velocity
u = 30 m/s

What does the

negative sign mean?

62

Worked Example 5

The velocity of a car increases from rest to 9 m/s in the first 3 s. Calculate its acceleration.

2.1 What Are Speed, Velocity and Acceleration?

63

Worked Example 5

The velocity of a car increases from rest to 9 m/s in the first 3 s. Calculate its acceleration.

2.1 What Are Speed, Velocity and Acceleration?

Solution

Given information:

Initial velocity u = 0 m/s

Initial velocity v = 9 m/s

Time taken t = 3 s

64

Let’s Understand

Refer to Textbook pg 25 for
Worked Example 2F & 2G

65

2.1 What Are Speed, Velocity and Acceleration?

Non-uniform Acceleration
• An object undergoes non-uniform acceleration when the change in the velocity of the

object per unit time is not the same.

Textbook
Page 26

Velocity increases /

decreases at a
changing rate

66

2.1 What Are Speed, Velocity and Acceleration?

Non-uniform Acceleration
• Note that the change in velocity is not the same for every second.
• The increase in distance travelled per second increases in a varying manner as the

moving object is travelling at non-uniform acceleration.

Textbook
Page 26

67

Worked Example

Describe the motion of the car below, in terms of its speed and acceleration.

2.1 What Are Speed, Velocity and Acceleration?

0

Time/s

3

60 m/s

Velocity

Velocity
Change

2

20 m/s

1

40 m/s

10 m/s

+30 m/s

–20 m/s

+40 m/s

68

Worked Example

Describe the motion of the car below, in terms of its speed and acceleration.

2.1 What Are Speed, Velocity and Acceleration?

Solution

❑ From t = 0 s to t = 1 s, the car accelerates from a speed of 10 m/s to 40 m/s.

❑ From t = 1 s to t = 2 s, the car decelerates from a speed of 40 m/s to 20 m/s.

❑ From t = 2 s to t = 3 s, the car accelerates from a speed of 20 m/s to 60 m/s.

0

Time/s

3

60 m/s

Velocity

Velocity
Change

2

20 m/s

1

40 m/s

10 m/s

+30 m/s

–20 m/s

+40 m/s

69

Consolidate
Learning

70

Let’s Practise 2.1

Check your understanding by trying
out the questions.

Textbook
Page 26

71

Critical Thinking Question

(a)

When a skydiver jumps out of the plane.

(b)

When a skydiver reaches terminal velocity.

(c)

When a skydiver opens the parachute.

(d)

When a skydiver lands on the ground.

When is acceleration the greatest in skydiving?

72

Enrichment

73

Cool Career

Sports Engineer
• What are some of the interesting aspects of

being a sports engineer?

• Do you know of any other professions that

require the knowledge of kinematics?

Textbook
Page 40

74

Lesson 2.2A
(double period)

75

Activate Prior Knowledge

Launch Quiz 2.2

Let’s play a quiz on your personal learning device to test your prior knowledge from
the past lessons!

76

Chapter 2 Kinematics

• 2.1 What Are Speed, Velocity and Acceleration?
• 2.2 How Do We Analyse Motion Graphically?
• 2.3 What Is Acceleration of Free Fall?

77

2.2 How Do We Analyse Motion Graphically?

Learning Outcome(s)
• Plot and interpret a distance–time graph and a speed–time graph for motion in

one direction.

• Deduce the motion of a body from the shape of a distance–time graph.
• Deduce the motion of a body from the shape of a speed–time graph.
• Calculate the area under a speed–time graph to determine the distance travelled

in one direction with uniform speed or uniform acceleration.

78

Capture Interest

79

Demonstration Using Datalogger

• Set up a datalogger with a motion sensor.
• Invite a student volunteer for the demonstration.
• Start the sensor once the student starts to walk away from

it. The distance is set to be 3 m.

• Ask the class to describe the motion and predict the shape

of the distance-time graph.

• Connect the datalogger to a projector to view the

distance-time graph.

Question:
What are the advantages of plotting graphs of motion?

Refer to chapter activity

(jsTracker) – to be done after

completion of 2.2A & 2.2B

80

Construct
Understanding

81

2.2 How Do We Analyse Motion Graphically?

Recall (gradient)

• The gradient measures the steepness of the graph

• In the diagrams below, which slope is steeper?

More
gentle

Steepe

r

Slope

A

Slope

B

Length of graph does not determine

the magnitude of the gradient

82

2.2 How Do We Analyse Motion Graphically?

Recall (gradient)

• In the diagrams below, describe the magnitude of the gradient for both persons.

Both gradients have the same

magnitude

Person

A

Person

B

Are the gradients positive or

negative?

83

2.2 How Do We Analyse Motion Graphically?

Recall (gradient)

• In the diagrams below, which graph has a positive gradient?

Positive
gradient

Negative
gradient

Graph

A

Graph

B

How do we calculate
(the magnitude of the)

gradient?

84

2.2 How Do We Analyse Motion Graphically?

Recall (gradient)

• In the diagrams below, what is the gradient for each graph?

Graph

A

Graph

B

85

2.2 How Do We Analyse Motion Graphically?

Recall (gradient)

• How to calculate the magnitude of the gradient from graph?

ris
e

run

86

2.2 How Do We Analyse Motion Graphically?

Distance–Time Graphs

distance / m

time / s

What does the gradient of a

distance-time graph represent?

Vertical axis

(front)

Horizontal axis

(back)

87

2.2 How Do We Analyse Motion Graphically?

Distance–Time Graphs
• The distance–time graph of an object gives us some information about the

motion of the object.

• The gradient of a distance–time graph of an object gives the speed of the object.

• There are four possible scenarios for the motion of a car travelling along a

straight line in one direction.

Textbook
Page 27

88

2.2 How Do We Analyse Motion Graphically?

Distance–Time Graphs
Scenario 1: Car at rest

Scenario 2: Car travelling at

a uniform speed of 10 m/s

Textbook
Page 27

89

2.2 How Do We Analyse Motion Graphically?

Distance–Time Graphs
Scenario 3: Car travelling with increasing
speed (non-uniform speed)

Textbook
Page 28

Scenario 4: Car travelling with decreasing
speed (non-uniform speed)

90

2.2 How Do We Analyse Motion Graphically?

Distance–Time Graphs (instantaneous speed)

Instantaneous speed

• describes how fast an object is at a particular time.

• equals the gradient of the tangent, at a specifictime

on the distance−time graph.

At t = 5 s, instantaneous speed is

= = 20.0 m/s
Δd1
Δt1

(100 – 0) m
(7.5 – 2.5) s

➊

At t = 10 s, instantaneous speed is

== 41.3 m/s
Δd2
Δt2

(290 – 125) m

(12 – 8) s

➋

Δd1

Δt1

➊

Δd2

Δt2

➋

Distance/m

91

2.2 How Do We Analyse Motion Graphically?

Distance–Time Graphs (instantaneous speed vs average speed)

Average speed after t = 8.5 s is

<v> =

=

= 17.7 m/s

total distance
total time taken
150 m
8.5 s

Instantaneousspeed at t = 8.5 s is

=

= 38.9 m/s
Δd
Δt

(220 – 80) m
(10.3 – 6.7) s

At a specific time

(t = 8.5 s)

For a time interval

(from t = 0 s to t = 8.5 s)

(10.3, 220)

(6.7, 80)

8.5

Distance/m

92

2.2 How Do We Analyse Motion Graphically?

Recall (gradient)

• In the diagram below, which graph(s) has/have a positive gradient?

decreasing gradient

increasing gradient

positive

negative

93

Distance–Time Graphs (deducing the motion of an object)

2.2 How Do We Analyse Motion Graphically?

Distance

Speed

Motion of object

Zero / non-zero

(constant)

Zero

(constant)
Object is at rest / not moving / stationary.

Increasing at a
constant rate

Zero

(constant)
Object is moving at a constant speed of … m/s.

Increasing at an
increasing rate
Increasing

Object is moving at an increasing speed.

Increasing at a
decreasing rate
Decreasing

Object is moving at a decreasing speed.

94

2.2 How Do We Analyse Motion Graphically?

Distance–Time Graphs (deducing the motion of an object)

Location

Graph is a/an …Gradient is …

Deduction

A
Horizontal
straight line
Zero
Object is at rest / not moving /
stationary.

B
Upward diagonal

straight line
Positive
Object is moving at a constant
speed of … m/s.

C
Horizontal

tangent
Zero

Object is instantaneously at
rest / has zero instantaneous
speed.

C to D

Downward curve

Increasing
Object is moving at increasing
speed in opposite direction.

D to E/F

Downward curve

Decreasing
Object is moving at decreasing
speed in opposite direction.

G
Horizontal
straight line
Zero
Object is at rest / not moving /
stationary.

Distance /
m

95

Worked Example 1

Describe the motion of the object:

2.2 How Do We Analyse Motion Graphically?

Distance / m

96

Worked Example 1

Describe the motion of the object:

2.2 How Do We Analyse Motion Graphically?

Solution

❑ From t = 0 s to t = 5 s, the object is moving with constant speed of 10 m/s.

❑ From t = 5 s to t = 8 s, the object is at rest.

❑ From t = 8 s to t = 10 s, the object is moving with constant speed of 25 m/s.

❑ From t = 10 s to t = 17 s, the object is moving with constant speed of 2.86 m/s (3 s.f.).

Distance / m

97

Worked Example 2

Describe the motion of the object:

2.2 How Do We Analyse Motion Graphically?

Distance / m

98

Worked Example 2

Describe the motion of the object:

2.2 How Do We Analyse Motion Graphically?

Solution

❑ From t = 0 s to t = 5 s, the object is moving with constant speed of 10 m/s.

❑ From t = 5 s to t = 10 s, the object is moving with increasing speed.

❑ From t = 10 s to t = 15 s, the object is moving with decreasing speed.

Distance / m

99

2.2 How Do We Analyse Motion Graphically?

Speed–Time Graphs

speed / m/s

time / s

What does the gradient of a
speed-time graph represent?

Vertical axis

(front)

Horizontal axis

(back)

100

10
0

2.2 How Do We Analyse Motion Graphically?

Speed–Time Graphs
• The speed–time graphs can be used to show uniform and non-uniform

acceleration of a car that is travelling along a straight line in one direction.

• The gradient of a speed–time graph of an object gives the acceleration of the

object.

Textbook
Page 28

101

10
1

Worked Example

Determine the acceleration of the object.

2.2 How Do We Analyse Motion Graphically?

speed /

m/s

102

10
2

Worked Example

Determine the acceleration of the object.

2.2 How Do We Analyse Motion Graphically?

speed /

m/s

103

10
3

2.2 How Do We Analyse Motion Graphically?

Speed–Time Graphs
Scenario 1: Car at rest

Scenario 2: Car travelling at a uniform

constant speed of 10 m/s

Textbook
Page 28

104

10
4

2.2 How Do We Analyse Motion Graphically?

Speed–Time Graphs
Scenario 3: Car travelling with uniform
acceleration

Textbook
Page 29

Scenario 4: Car travelling with uniform
deceleration

105

10
5

2.2 How Do We Analyse Motion Graphically?

Speed–Time Graphs
Scenario 5: Car travelling with increasing
acceleration (non-uniform acceleration)

Textbook
Page 29

Scenario 6: Car travelling with decreasing
acceleration (non-uniform acceleration)

106

10
6

2.2 How Do We Analyse Motion Graphically?

Speed–Time Graphs (instantaneous acceleration)

Instantaneous acceleration

• describes the acceleration of an object is at a particular

time.

• equals the gradient of the tangent, at a specifictime on

the speed−time graph.

Instantaneous acceleration at t = 3 s is

= 12.5 m/s2

Δv
Δt

(30 – 5) m/s

(4 – 2) s
=

speed /
m/s

107

10
7

Worked Example

Look at the following speed-time graph showing the velocity of an MRT train
travelling between two stations. Describe its motion at each time interval.

2.2 How Do We Analyse Motion Graphically?

Velocity /

m/s

Time / s

speed / m/s

108

10
8

Worked Example

Look at the following speed-time graph showing the speed of an MRT train
travelling between two stations. Describe its motion at each time interval.

2.2 How Do We Analyse Motion Graphically?

Solution

❑ From t = 0 s to t = 20 s, the train is moving at constant acceleration of 1.5 m/s2.

❑ From t = 20 s to t = 90 s, the train is moving at zero acceleration.

❑ From t = 90 s to t = 120 s, the train is moving at constant acceleration of – 1.0 m/s2.

speed / m/s

109

10
9

2.2 How Do We Analyse Motion Graphically?

Question:
Can you describe the motion of an object, at sections A to E, for the following
speed-time graph?

Speed / m/s

Time / s

A

B

D
C

E

110

11
0

2.2 How Do We Analyse Motion Graphically?

Comparisons Between Distance–Time and Speed–Time Graphs

Textbook
Page 30

111

11
1

Let’s Understand

Refer to Textbook pg 31 &
32 for Worked Example 2H

& 2I

112

11
2

Summary of Lesson 2.2A

• The distance-time graph and speed-time graph provide information about the

motion of an object.

• The gradient of a distance–time graph of an object gives the speed of the object.

• The gradient of a speed–time graph of an object gives the acceleration of the

object.

113

11
3

Lesson 2.2B
(single period)

114

11
4

2.2 How Do We Analyse Motion Graphically?

Recall (distance)

• What is the formula for calculating distance?

distance

speed

time

distance = speed × time

What is an assumption that must be
made when applying this formula?

115

11
5

2.2 How Do We Analyse Motion Graphically?

Recall (distance)

• What is the distance travelled by a car if it travels at a constant speed of 25 m/s

in a straight line for 5 s?

Solution

distance = speed × time = 25 × 5 = 125 m

How will you sketch the distance-time
graph and speed-time graph of this car?

116

11
6

2.2 How Do We Analyse Motion Graphically?

Recall (distance)

• Sketch the distance-time graph and speed-time graph of a car travelling at a

constant speed of 25 m/s in a straight line for 5 s.

speed / m/s

time / s

“constant speed of 25 m/s in a straight line” is the

same as saying “constant velocity of 25 m/s”

distance / m

time / s

25

5

125

distance = speed × time = 25 × 5 = 125 m

0

What resemblance do

you observe here?

A “constant speed” implies a “constant

gradient of a distance-time graph”

117

11
7

2.2 How Do We Analyse Motion Graphically?

Area Under Speed–Time Graph
• The area under the speed-time graph gives the distance of the object.

Textbook
Page 33

118

11
8

Area Under Speed–Time Graph
• The area under the speed–time graph gives the distance of the object.

2.2 How Do We Analyse Motion Graphically?

speed / m/s

time / s

A

Distance
= area under speed-time graph
= (0 m/s)(5 s)
= 0 m

A

speed / m/s

time / s

B

Distance
= area under speed-time graph
= (10 m/s)(5 s)
= 50 m

B

119

11
9

Area Under Speed–Time Graph
• The area under the speed–time graph gives the distance of the object.

2.2 How Do We Analyse Motion Graphically?

speed/m/s

Time/s

speed / m/s

time / s

C

D

C

D

120

12
0

2.2 How Do We Analyse Motion Graphically?

Worked Example

• The v-t graph shows the motion of a car.

a)

What is the acceleration of the car from:

(i)

t = 0 s to 2 s

(ii) t = 2 s to 4 s

(iii) t = 4 s to 6 s

(iv) t = 6 s to 8s

(v) t = 8 s to 12 s

speed / m/s

121

12
1

2.2 How Do We Analyse Motion Graphically?

Worked Example

• The v-t graph shows the motion of a car.

a)

What is the acceleration of the car from:

Solution

(i)

t = 0 s to 2 s

(ii) t = 2 s to 4 s

(iii) t = 4 s to 6 s

(iv) t = 6 s to 8s

(v) t = 8 s to 12 s

a = 0 m/s2

a = 15 m/s2

a = 0 m/s2

a = – 10 m/s2

a = – 5 m/s2

Describe the change in the

acceleration from t = 6 s to t = 12 s.

speed / m/s

122

12
2

2.2 How Do We Analyse Motion Graphically?

Worked Example

• The v-t graph shows the motion of a car.

b)

What is the distance travelled by the car from t = 8 s to t = 12 s?

speed / m/s

123

12
3

2.2 How Do We Analyse Motion Graphically?

Consider the following speed-time graph for an object:

Textbook
Page 34

speed / m/s

124

12
4

Let’s Understand

Refer to Textbook pg 35 &
36 for Worked Example 2J

& 2K

125

12
5

Consolidate
Learning

126

12
6

Let’s Practise 2.2

Check your understanding by trying
out the questions.

Textbook
Page 37

127

12
7

Enrichment

128

12
8

Enrichment

• A food delivery company has

embarked on a collaboration with a
company to use drones for food
delivery.

• A drone is routed to fly along the

shortest distance to the destination.

• What are the potential uses for

drones?

• Can you think of the challenges or

limitations of using drones?

129

12
9

Lesson 2.3A
(double period)

130

13
0

Activate Prior Knowledge

Launch Quiz 2.3

Let’s play a quiz on your personal learning device to test your prior knowledge from
the past lessons!

131

13
1

Chapter 2 Kinematics

• 2.1 What Are Speed, Velocity and Acceleration?
• 2.2 How Do We Analyse Motion Graphically?
• 2.3 What Is Acceleration of Free Fall?

132

13
2

2.3 What Is Acceleration of Free Fall?

Learning Outcome(s)
• State that the acceleration of free fall for a body near to Earth is constant and is

approximately 10 m/s2.

133

13
3

Capture Interest

134

13
4

Which object will reach the ground first?

Questions:
1.

In the first experiment, which object will
reach the ground first?

2.

In the absence of air resistance, which object
will reach the ground first?

135

13
5

Construct
Understanding

136

13
6

2.3 What Is Acceleration of Free Fall?

Acceleration due to gravity, g
• All objects, regardless of mass or size, fall at the same acceleration

due to the Earth’s gravity.

• Assuming that the only force acting on an object is due to gravity

(ignoring air resistance), it is said to be in free fall.

• Acceleration due to gravity (free fall) is constant and acts in a

downward direction.

• For objects close to Earth’s surface, the value of g is generally taken to

be 9.8 m/s2., assuming negligible air resistance.

• For simplicity in calculations, we take this value to be approximately

10 m/s2, unless otherwise stated.

Textbook
Page 38

137

13
7

2.3 What Is Acceleration of Free Fall?

Textbook
Page 38

Question:
Which observer is correct about the man and the girl? Explain why.

138

13
8

Let’s Understand

Refer to Textbook pg 38 for

Worked Example 2L

139

13
9

Let’s Practise 2.3

Check your understanding by trying
out the questions.

Textbook
Page 39

140

14
0

Lesson 2.3B
(single period)

141

14
1

Consolidate
Learning

142

14
2

What Have
You
Learnt?

Textbook
Page 41

143

14
3

Distance–Time and Speed-Time Graphs

Deducing the motion of an object

Distance

Speed

Acceleration

Motion of object

Constant

(zero / non-zero)

Zero

(constant)

Zero

(constant)
Object is at rest / not moving / stationary.

Increasing at a
constant rate

Non-zero
(constant)

Zero

(constant)
Object is moving at a constant speed of … m/s.

Increasing at an
increasing rate

Increasing at a
constant rate

Positive
(constant)

Object is moving at an increasing speed (with a constant

acceleration of … m/s2).

Increasing at an
increasing rate

Positive

(increasing)

Object is moving at an increasing speed (with an increasing

acceleration).

Increasing at an
increasing rate

Increasing at a
decreasing rate

Positive

(decreasing)

Object is moving at an increasing speed (with a decreasing

acceleration).

144

14
4

Distance–Time and Speed-Time Graphs

Deducing the motion of an object

Distance

Speed

Acceleration

Motion of object

Increasing at a
decreasing rate

Decreasing at a
constant rate

Negative
(constant)

Object is moving at a decreasing speed (with a constant

acceleration of … m/s2).

Increasing at a
decreasing rate

Decreasing at
an increasing

rate

Negative

(increasing)

Object is moving at a decreasing speed (with an increasing

acceleration).

Increasing at a
decreasing rate

Decreasing at a
decreasing rate

Negative

(decreasing)

Object is moving at a decreasing speed (with a decreasing

acceleration).

145

14
5

Let’s Review

Check your understanding by trying
out the question(s).

146

14
6

Let’s Assess
Let’s Reflect

Check your understanding by
trying out the question(s).

147

14
7

Lesson 2.3C
(double period)

148

14
8

Enrichment

149

14
9

Problem-based Learning Activity

•In your teams, propose solutions to reduce the number of traffic
accidents at pedestrian crossings.

- Use the guiding questions in the Textbook to help you in
coming up with a proposal.
•Then, structure your thought process using the Problem-based Learning
Activity: Application in the Theory Workbook.
•Finally, carry out the STEM Project in the Practical Workbook.

Textbook
Page 40

150

15
0

Acknowledgements

•Slide 9: Usain Bolt © photoyh | Shutterstock.com, cheetah running – ID 70320512 © Svetlana Foote | Dreamstime.com, empty road © ssguy | Shutterstock.com

2023 O SCIPHY 02 Kinematics Teaching Slides

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