Acceleration and velocitytime graphs - Teacher Slides.pptx

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Acceleration and velocity–time graphs

Forces

Lesson 12 of 20

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Warm-up

Forces

Lesson 12 of 20

Answer each one, then check.

1

What is velocity?

2

What is the unit of acceleration?

3

What does deceleration mean?

4

What is the gradient of a graph?

5

What is the acceleration of free fall near Earth?

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Warm-up - Answers

Forces

Lesson 12 of 20

1

What is velocity?

Speed in a given direction

2

What is the unit of acceleration?

Metres per second squared (m/s²)

3

What does deceleration mean?

Slowing down

4

What is the gradient of a graph?

Change in y divided by change in x

5

What is the acceleration of free fall near Earth?

About 9.8 m/s²

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Learning Objectives

Forces

Lesson 12 of 20

1

Recall and apply a = Δv ÷ t.

2

Draw and interpret velocity–time graphs.

3

Use the gradient to find acceleration.

4

Use the area under a velocity–time graph to find distance (Higher tier).

5

Apply v² − u² = 2as.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Forces

Lesson 12 of 20

ACCELERATION

acceleration = change in velocity ÷ time taken a = Δv/t

For uniform acceleration v² − u² = 2as (given on the equation sheet). Near Earth's surface a freely falling object accelerates at about 9.8 m/s².

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

A Velocity–Time Graph

Forces

Lesson 12 of 20

Gradient = acceleration; area = distance.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Calculating Acceleration

Forces

Lesson 12 of 20

A car accelerates from rest to 12 m/s in 4.0 s. Calculate its acceleration.

1

Change in velocity

12 − 0 = 12 m/s

2

Substitute

a = 12 ÷ 4.0

3

Answer

a = 3.0 m/s²

ANSWER

3.0 m/s²

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Using v² − u² = 2as

Forces

Lesson 12 of 20

A car starts at 10 m/s and accelerates at 2.0 m/s² over a distance of 100 m. Calculate the final speed.

1

Write the equation

v² − u² = 2as

2

Substitute

v² − 10² = 2 × 2.0 × 100

3

Rearrange

v² = 100 + 400 = 500

4

Square root

v = 22.4 m/s

ANSWER

22 m/s (2 s.f.)

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Area Under a Graph (Higher)

Forces

Lesson 12 of 20

Use the graph (accelerating from 0 to 10 m/s in 5 s, constant for 10 s, then stopping in 5 s) to find the distance travelled.

1

Section 1 (triangle)

½ × 5 × 10 = 25 m

2

Section 2 (rectangle)

10 × 10 = 100 m

3

Section 3 (triangle)

½ × 5 × 10 = 25 m

4

Total

25 + 100 + 25 = 150 m

ANSWER

150 m

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Free Fall

Forces

Lesson 12 of 20

A ball is dropped from rest from a height of 20 m. Ignoring air resistance, calculate its speed on landing. a = 9.8 m/s².

1

Write the equation

v² = 2as

2

Substitute

v² = 2 × 9.8 × 20 = 392

3

Answer

v = 19.8 m/s

ANSWER

19.8 m/s

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Reading the Graph

Forces

Lesson 12 of 20

Key features.

Gradient

The acceleration; negative gradient means deceleration.

Horizontal line

Constant velocity (zero acceleration).

Area

Distance travelled (Higher tier); count squares for curves.

Units

m/s for velocity, m/s² for acceleration.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Key Terms

Forces

Lesson 12 of 20

Acceleration

The rate of change of velocity.

Deceleration

Slowing down.

Velocity–time graph

A graph of velocity against time.

Uniform acceleration

Constant acceleration.

Free fall

Falling under gravity alone.

Gradient

How steep a line is.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Forces

Lesson 12 of 20

YOUR TASK

Acceleration Practice

12 minutes

A train slows from 30 m/s to 10 m/s in 50 s. Calculate its acceleration. What does the sign tell you?

1

Change in velocity.

2

Divide by time.

WHAT A GOOD ANSWER SHOWS

a = (10 − 30) ÷ 50 = −0.40 m/s². The negative value shows deceleration.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Can I...?

Forces

Lesson 12 of 20

Recall a = Δv ÷ t.

Calculate acceleration.

Use the gradient of a v–t graph.

Use the area under a v–t graph.

Use v² − u² = 2as.

Estimate everyday accelerations.

Give units.

Read a graph.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Summary & Exam Focus

a = Δv ÷ t.

v² − u² = 2as.

v–t gradient = acceleration; area = distance.

Free fall: a ≈ 9.8 m/s².

EXAM FOCUS

A car accelerates from rest to 12 m/s in 4.0 s. Calculate the acceleration. (2 marks)

Divide the change in velocity by time.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Exam Practice: Acceleration and velocity–time graphs

Forces

Lesson 12 of 20

Answer all questions. Use the mark allocation as a guide to how much to write. · 16 minutes

Question 1 · 2 marks · Calculate

A car accelerates from rest to a velocity of 12 m/s in 4.0 s. Calculate the acceleration of the car. Use the equation: acceleration =…

Question 2 · 4 marks · Use the graph

The graph shows the velocity of a cyclist. (a) Calculate the acceleration in the first 5 s. (b) Describe the motion between 5 s and 15 s.

Question 3 · 3 marks · Calculate

A car starts at 10 m/s and accelerates uniformly at 2.0 m/s² over a distance of 100 m. Calculate its final velocity. Use the equation…

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Exam Practice: Acceleration and velocity–time graphs (cont.)

Forces

Lesson 12 of 20

Question 4 · 3 marks · Calculate

Use the velocity–time graph in question 2 to calculate the total distance travelled by the cyclist.

Question 5 · 3 marks · Calculate

A ball is dropped from rest from a height of 20 m. Assume no air resistance. The acceleration of free fall is 9.8 m/s². Calculate the speed…

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 1 · 2 marks · Calculate

Forces

Lesson 12 of 20

“

A car accelerates from rest to a velocity of 12 m/s in 4.0 s. Calculate the acceleration of the car. Use the equation: acceleration = change in velocity ÷ time taken

HOW TO ANSWER IT

Command word: Calculate. Worth 2 marks, so plan before writing.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 1 · mark scheme

Forces

Lesson 12 of 20

2 marks available. Award a mark for each point made.

Correct substitution

1 mark

3.0 m/s²

1 mark

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 2 · 4 marks · Use the graph

Forces

Lesson 12 of 20

The graph shows the velocity of a cyclist. (a) Calculate the acceleration in the first 5 s. (b) Describe the motion between 5 s and 15 s. (4 marks)

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 2 · mark scheme

Forces

Lesson 12 of 20

4 marks available. Award a mark for each point made.

Change in velocity 10 m/s

1 mark

2.0 m/s²

1 mark

Constant velocity

1 mark

10 m/s

1 mark

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 3 · 3 marks · Calculate

Forces

Lesson 12 of 20

“

A car starts at 10 m/s and accelerates uniformly at 2.0 m/s² over a distance of 100 m. Calculate its final velocity. Use the equation: (final velocity)² − (initial velocity)² = 2 × acceleration × distance

HOW TO ANSWER IT

Command word: Calculate. Worth 3 marks, so plan before writing.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 3 · mark scheme

Forces

Lesson 12 of 20

3 marks available. Award a mark for each point made.

Correct substitution

1 mark

v² = 500

1 mark

22 m/s

1 mark

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 4 · 3 marks · Calculate

Forces

Lesson 12 of 20

“

Use the velocity–time graph in question 2 to calculate the total distance travelled by the cyclist.

HOW TO ANSWER IT

Command word: Calculate. Worth 3 marks, so plan before writing.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 4 · mark scheme

Forces

Lesson 12 of 20

3 marks available. Award a mark for each point made.

Areas of the three sections

1 mark

25 + 100 + 25

1 mark

150 m

1 mark

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 5 · 3 marks · Calculate

Forces

Lesson 12 of 20

“

A ball is dropped from rest from a height of 20 m. Assume no air resistance. The acceleration of free fall is 9.8 m/s². Calculate the speed of the ball when it lands.

HOW TO ANSWER IT

Command word: Calculate. Worth 3 marks, so plan before writing.

openrevise.com

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 5 · mark scheme

Forces

Lesson 12 of 20

3 marks available. Award a mark for each point made.

Uses v² = 2as

1 mark

392

1 mark

19.8 m/s

1 mark

openrevise.com