Linear Motion

Linear Motion — Physics Form 4

PHYSICS • Form 4 • Chapter 2: Force and Motion I

Linear Motion

Linear motion is motion in a straight line, described by distance, displacement, speed, velocity, and acceleration. It can be uniform (constant velocity) or non-uniform (acceleration). These quantities help analyze how objects move, from everyday vehicles to laboratory experiments using tools like ticker timers and photogate systems.

Learning Objectives

Define and differentiate between distance, displacement, speed, velocity, and acceleration.
Compare scalar (distance, speed) and vector (displacement, velocity, acceleration) quantities.
Use formulas to calculate speed, velocity, and acceleration.
Explain the operation of ticker timers and photogate systems for studying linear motion.
Solve problems involving linear motion using the four linear motion equations.

Distance vs Displacement

See the difference between the total path length (distance) and the shortest straight-line distance with direction (displacement).

Explore Car Motion

Change the acceleration and see how velocity and displacement change. Compare the car position and the v-t graph side by side.

v against t graph

Acceleration, a 2 m/s²

decelerateaccelerate

Fixed values: u = 5 m/s, t = 5 s.

Initial velocity, u5 m/s

Final velocity, v15 m/s

Displacement, s35 m

Accelerating

Positive acceleration. The car is speeding up. Velocity increases over time.

Formulav = u + at

Formulas = ut + ½at²

Gradient= a

Linear Motion Simulation — Print Reference

Fixed values: u = 5 m/s, t = 5 s. Adjustable: acceleration, a (−1 to 10 m/s²).

a / m s ⁻²	v = u + at / m s ⁻¹	s = ut + ½at² / m
−1	0	10
0	5	25
2	15	35
5	30	75
10	55	150

Short Explanation

Key Quantities

Distance is the length of the route covered (scalar). Displacement is the shortest straight-line distance with direction (vector).

Speed and Velocity

Speed is the rate of change of distance (scalar): \(\text{speed} = \dfrac{\text{distance}}{\text{time}}\). Velocity is the rate of change of displacement (vector): \(v = \dfrac{s}{t}\).

Acceleration

Acceleration is the rate of change of velocity (vector): \(a = \dfrac{v - u}{t}\). A negative acceleration means the object is slowing down (deceleration).

Uniform vs Non-Uniform Velocity

Uniform velocity: Displacement increases equally over time (constant speed and direction). Non-uniform velocity: Displacement changes unequally over time (acceleration occurs).

Quantity	Type	Formula	SI Unit
Distance	Scalar	speed × time	m
Displacement	Vector	\(v \times t\)	m
Speed	Scalar	\(\dfrac{\text{distance}}{t}\)	m s ⁻¹
Velocity	Vector	\(\dfrac{s}{t}\)	m s ⁻¹
Acceleration	Vector	\(\dfrac{v - u}{t}\)	m s ⁻²

Tools for Studying Linear Motion

Ticker Timer: Uses 50 Hz AC to make 50 ticks per second (1 tick = 0.02 s). Records displacement over time on ticker tape.

Photogate System: More accurate than ticker timers (measures time to 0.001 s) by detecting object passage without friction.

Four Linear Motion Equations (Uniform Acceleration)

1 \(v = u + at\) — relates v, u, a, t

2 \(s = \dfrac{1}{2}(u + v)t\) — relates s, average velocity, t

3 \(s = ut + \dfrac{1}{2}at^2\) — relates s, u, a, t

4 \(v^2 = u^2 + 2as\) — relates v, u, a, s

iu = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time

Try to Answer First

Answer in your mind, then press “Check Answer”.

A car moving at 30 m/s stops after 5 s. What is its acceleration?

Check Answer

Answer: \(a = \dfrac{v - u}{t} = \dfrac{0 - 30}{5} = -6\ \mathrm{m\,s^{-2}}\). The negative sign indicates deceleration (opposite direction to motion).

Differentiate between distance and displacement.

Check Answer

Answer: Distance is the total route length (scalar quantity). Displacement is the shortest straight-line distance between initial and final positions with a specific direction (vector quantity).

A transporter accelerates from 1 m/s to 5 m/s in 0.5 minutes. Calculate its displacement.

Check Answer

Answer: Convert 0.5 minutes to 30 s. \(s = \dfrac{1}{2}(u + v)t = \dfrac{1}{2}(1 + 5)(30) = 90\ \mathrm{m}\).

Common Mistakes

!Confusing distance (scalar) with displacement (vector) — using total route length instead of straight-line distance.
!Mixing up speed (scalar) and velocity (vector) — ignoring direction in velocity.
!Forgetting sign conventions for acceleration — negative acceleration means opposite direction to motion (deceleration).

Concept Misunderstandings

Misunderstanding

Acceleration always means speeding up.

Correct Concept

Acceleration can be positive (speeding up) or negative (slowing down, deceleration). The sign indicates direction relative to motion.

Misunderstanding

Distance and displacement are the same.

Correct Concept

Distance depends on the path taken; displacement depends only on the initial and final positions and direction.

Summary

Linear motion is motion in a straight line, described by distance (scalar), displacement (vector), speed (scalar), velocity (vector), and acceleration (vector).
Uniform velocity has constant speed and direction; non-uniform velocity involves acceleration.
Ticker timers make 50 ticks per second (1 tick = 0.02 s); photogate systems measure time to 0.001 s without friction.
The four linear motion equations solve problems with uniform acceleration: \(v = u + at\), \(s = \dfrac{1}{2}(u + v)t\), \(s = ut + \dfrac{1}{2}at^2\), \(v^2 = u^2 + 2as\).
Negative acceleration indicates deceleration (opposite direction to motion).

Short Activity

Objective: Test understanding of scalar vs. vector quantities and linear motion formulas.

A. Objective Quiz

1 Which of the following is a vector quantity?

Distance Speed Displacement Time

2 A ticker timer operating at 50 Hz produces how many ticks per second?

50 0.02 100 25

B. Fill in the Blanks

3 A car travels 100 km north. Its is 100 km north.

4 The of a car is the total distance it travels divided by time.

5 Acceleration is a quantity.

C. Matching / Drag and Drop

Drag each scalar quantity to its matching vector quantity. If using a phone, tap the answer first, then tap the matching box.

Scalar Quantities (Choices)

Distance

Speed

Time

Vector Quantities (Match)

1 Displacement — shortest straight-line distance with direction

2 Velocity — rate of change of displacement

3 Acceleration — rate of change of velocity

Keywords

Distance Displacement Speed Velocity Acceleration Ticker Timer Photogate System

Linear Motion

Linear Motion — Physics Form 4

PHYSICS • Form 4 • Chapter 2: Force and Motion I

Linear Motion

Learning Objectives

Define and differentiate between distance, displacement, speed, velocity, and acceleration.
Compare scalar (distance, speed) and vector (displacement, velocity, acceleration) quantities.
Use formulas to calculate speed, velocity, and acceleration.
Explain the operation of ticker timers and photogate systems for studying linear motion.
Solve problems involving linear motion using the four linear motion equations.

Distance vs Displacement

See the difference between the total path length (distance) and the shortest straight-line distance with direction (displacement).

Explore Car Motion

Change the acceleration and see how velocity and displacement change. Compare the car position and the v-t graph side by side.

v against t graph

Acceleration, a 2 m/s²

decelerateaccelerate

Fixed values: u = 5 m/s, t = 5 s.

Initial velocity, u5 m/s

Final velocity, v15 m/s

Displacement, s35 m

Accelerating

Positive acceleration. The car is speeding up. Velocity increases over time.

Formulav = u + at

Formulas = ut + ½at²

Gradient= a

Linear Motion Simulation — Print Reference

Fixed values: u = 5 m/s, t = 5 s. Adjustable: acceleration, a (−1 to 10 m/s²).

a / m s ⁻²	v = u + at / m s ⁻¹	s = ut + ½at² / m
−1	0	10
0	5	25
2	15	35
5	30	75
10	55	150

Short Explanation

Key Quantities

Distance is the length of the route covered (scalar). Displacement is the shortest straight-line distance with direction (vector).

Speed and Velocity

Speed is the rate of change of distance (scalar): \(\text{speed} = \dfrac{\text{distance}}{\text{time}}\). Velocity is the rate of change of displacement (vector): \(v = \dfrac{s}{t}\).

Acceleration

Acceleration is the rate of change of velocity (vector): \(a = \dfrac{v - u}{t}\). A negative acceleration means the object is slowing down (deceleration).

Uniform vs Non-Uniform Velocity

Uniform velocity: Displacement increases equally over time (constant speed and direction). Non-uniform velocity: Displacement changes unequally over time (acceleration occurs).

Quantity	Type	Formula	SI Unit
Distance	Scalar	speed × time	m
Displacement	Vector	\(v \times t\)	m
Speed	Scalar	\(\dfrac{\text{distance}}{t}\)	m s ⁻¹
Velocity	Vector	\(\dfrac{s}{t}\)	m s ⁻¹
Acceleration	Vector	\(\dfrac{v - u}{t}\)	m s ⁻²

Tools for Studying Linear Motion

Ticker Timer: Uses 50 Hz AC to make 50 ticks per second (1 tick = 0.02 s). Records displacement over time on ticker tape.

Photogate System: More accurate than ticker timers (measures time to 0.001 s) by detecting object passage without friction.

Four Linear Motion Equations (Uniform Acceleration)

1 \(v = u + at\) — relates v, u, a, t

2 \(s = \dfrac{1}{2}(u + v)t\) — relates s, average velocity, t

3 \(s = ut + \dfrac{1}{2}at^2\) — relates s, u, a, t

4 \(v^2 = u^2 + 2as\) — relates v, u, a, s

iu = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time

Try to Answer First

Answer in your mind, then press “Check Answer”.

A car moving at 30 m/s stops after 5 s. What is its acceleration?

Check Answer

Answer: \(a = \dfrac{v - u}{t} = \dfrac{0 - 30}{5} = -6\ \mathrm{m\,s^{-2}}\). The negative sign indicates deceleration (opposite direction to motion).

Differentiate between distance and displacement.

Check Answer

Answer: Distance is the total route length (scalar quantity). Displacement is the shortest straight-line distance between initial and final positions with a specific direction (vector quantity).

A transporter accelerates from 1 m/s to 5 m/s in 0.5 minutes. Calculate its displacement.

Check Answer

Answer: Convert 0.5 minutes to 30 s. \(s = \dfrac{1}{2}(u + v)t = \dfrac{1}{2}(1 + 5)(30) = 90\ \mathrm{m}\).

Common Mistakes

!Confusing distance (scalar) with displacement (vector) — using total route length instead of straight-line distance.
!Mixing up speed (scalar) and velocity (vector) — ignoring direction in velocity.
!Forgetting sign conventions for acceleration — negative acceleration means opposite direction to motion (deceleration).

Concept Misunderstandings

Misunderstanding

Acceleration always means speeding up.

Correct Concept

Acceleration can be positive (speeding up) or negative (slowing down, deceleration). The sign indicates direction relative to motion.

Misunderstanding

Distance and displacement are the same.

Correct Concept

Distance depends on the path taken; displacement depends only on the initial and final positions and direction.

Summary

Linear motion is motion in a straight line, described by distance (scalar), displacement (vector), speed (scalar), velocity (vector), and acceleration (vector).
Uniform velocity has constant speed and direction; non-uniform velocity involves acceleration.
Ticker timers make 50 ticks per second (1 tick = 0.02 s); photogate systems measure time to 0.001 s without friction.
The four linear motion equations solve problems with uniform acceleration: \(v = u + at\), \(s = \dfrac{1}{2}(u + v)t\), \(s = ut + \dfrac{1}{2}at^2\), \(v^2 = u^2 + 2as\).
Negative acceleration indicates deceleration (opposite direction to motion).

Short Activity

Objective: Test understanding of scalar vs. vector quantities and linear motion formulas.

A. Objective Quiz

1 Which of the following is a vector quantity?

Distance Speed Displacement Time

2 A ticker timer operating at 50 Hz produces how many ticks per second?

50 0.02 100 25

B. Fill in the Blanks

3 A car travels 100 km north. Its is 100 km north.

4 The of a car is the total distance it travels divided by time.

5 Acceleration is a quantity.

C. Matching / Drag and Drop

Drag each scalar quantity to its matching vector quantity. If using a phone, tap the answer first, then tap the matching box.

Scalar Quantities (Choices)

Distance

Speed

Time

Vector Quantities (Match)

1 Displacement — shortest straight-line distance with direction

2 Velocity — rate of change of displacement

3 Acceleration — rate of change of velocity

Keywords

Distance Displacement Speed Velocity Acceleration Ticker Timer Photogate System

Linear Motion

Linear Motion

Learning Objectives

Distance vs Displacement

Explore Car Motion

v against t graph

Accelerating

Linear Motion Simulation — Print Reference

Short Explanation

Key Quantities

Speed and Velocity

Acceleration

Uniform vs Non-Uniform Velocity

Tools for Studying Linear Motion

Four Linear Motion Equations (Uniform Acceleration)

Try to Answer First

Common Mistakes

Concept Misunderstandings

Summary

Short Activity

A. Objective Quiz

B. Fill in the Blanks

C. Matching / Drag and Drop

Keywords

Linear Motion

Linear Motion

Learning Objectives

Distance vs Displacement

Explore Car Motion

v against t graph

Accelerating

Linear Motion Simulation — Print Reference

Short Explanation

Key Quantities

Speed and Velocity

Acceleration

Uniform vs Non-Uniform Velocity

Tools for Studying Linear Motion

Four Linear Motion Equations (Uniform Acceleration)

Try to Answer First

Common Mistakes

Concept Misunderstandings

Summary

Short Activity

A. Objective Quiz

B. Fill in the Blanks

C. Matching / Drag and Drop

Keywords

Chapter : Force and Motion I

Topic : Linear Motion

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