Distancetime graphs - Teacher Slides.pptx

AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Distance–time graphs

Forces

Lesson 11 of 20

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Warm-up

Forces

Lesson 11 of 20

Answer each one, then check.

1

What is the gradient of a graph?

2

What does a horizontal line on a distance-time graph mean?

3

What is speed?

4

What is acceleration?

5

What does a steeper line mean?

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Warm-up - Answers

Forces

Lesson 11 of 20

1

What is the gradient of a graph?

Change in y divided by change in x

2

What does a horizontal line on a distance-time graph mean?

The object is stationary

3

What is speed?

Distance divided by time

4

What is acceleration?

Rate of change of velocity

5

What does a steeper line mean?

A faster speed

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Learning Objectives

Forces

Lesson 11 of 20

1

Draw distance–time graphs from measurements.

2

Interpret lines and slopes of distance–time graphs.

3

Calculate speed from the gradient of a distance–time graph.

4

Find the speed of an accelerating object at an instant using a tangent (Higher tier).

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Forces

Lesson 11 of 20

DISTANCE–TIME GRAPHS

The gradient of a distance–time graph is the speed of the object.

A straight line means constant speed, a horizontal line means stationary, and a curve means the speed is changing.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Reading a Distance–Time Graph

Forces

Lesson 11 of 20

Gradient = change in distance ÷ change in time.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

What the Graph Shows

Forces

Lesson 11 of 20

Learn these.

Shape

Meaning

Straight line sloping up

Constant speed

Horizontal line

Stationary

Steeper line

Higher speed

Curve getting steeper

Accelerating

Curve getting shallower

Decelerating

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Speed from a Gradient

Forces

Lesson 11 of 20

An object travels 40 m in the first 20 s. Calculate its speed from the graph.

1

Gradient

(change in distance)/(change in time)

2

Substitute

40/20

3

Answer

2.0 m/s

ANSWER

2.0 m/s

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Describing a Journey

Forces

Lesson 11 of 20

Describe the motion shown from 20 s to 40 s where the line is horizontal.

1

Distance

Does not change

2

Speed

Zero

ANSWER

The object is stationary.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Tangent (Higher)

Forces

Lesson 11 of 20

The distance is given by s = 0.5t² (in metres, t in seconds). Find the speed at t = 6 s using a tangent.

1

Draw a tangent

Touching the curve at t = 6 s

2

Gradient of the tangent

Δs/Δt from two points on the tangent: about 6 m/s

3

Check

The speed is t = 6 m/s from s = 0.5t²

ANSWER

About 6 m/s.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Drawing Graphs

Forces

Lesson 11 of 20

Good practice.

Axes

Time on the x-axis, distance on the y-axis, with units.

Points

Plot from a table, then join with a ruler (or a smooth curve if the speed changes).

Gradient

Use a large triangle for accuracy.

Units

m/s if distance in m and time in s.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Key Terms

Forces

Lesson 11 of 20

Distance–time graph

A graph of distance against time.

Gradient

How steep a line is.

Stationary

Not moving.

Tangent

A straight line that touches a curve at one point.

Constant speed

The same speed all the time.

Accelerating

Speeding up.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Forces

Lesson 11 of 20

YOUR TASK

Story Graph

12 minutes

A cyclist travels 100 m in 20 s, stops for 20 s and then travels 60 m in 20 s. Sketch the graph and calculate the speed in each part.

1

Plot the three sections.

2

Gradient for each.

WHAT A GOOD ANSWER SHOWS

Part 1: 5.0 m/s. Part 2: 0 m/s. Part 3: 3.0 m/s.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Can I...?

Forces

Lesson 11 of 20

Draw a distance–time graph.

Say what a horizontal line means.

Calculate speed from a gradient.

Compare speeds from slopes.

Describe a journey.

Describe a curve.

Draw a tangent.

Use units.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Summary & Exam Focus

Gradient = speed.

Horizontal line = stationary.

Steeper = faster.

Higher: tangent to a curve gives instantaneous speed.

EXAM FOCUS

The graph shows 100 m in 20 s. Calculate the speed in the first 20 s. (2 marks)

Gradient = distance ÷ time.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Exam Practice: Distance–time graphs

Forces

Lesson 11 of 20

Answer all questions. Use the mark allocation as a guide to how much to write. · 15 minutes

Question 1 · 4 marks · Use the graph

The graph shows the distance travelled by a cyclist. (a) Calculate the speed in the first 20 s. (b) Describe the motion between 20 s and 40…

Question 2 · 2 marks · State

Describe what the gradient of a distance–time graph represents and what a horizontal line shows.

Question 3 · 3 marks · Calculate

A car travels 120 m in 10 s at constant speed. Sketch a distance–time graph for this and calculate the gradient.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Exam Practice: Distance–time graphs (cont.)

Forces

Lesson 11 of 20

Question 4 · 2 marks · Explain

The distance–time graph for a runner is a curve that gets steeper. Describe the motion.

Question 5 · 3 marks · Determine

The graph shows the distance of a car from a starting point against time as a curve. Describe how to find the speed at a particular time.

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 1 · 4 marks · Use the graph

Forces

Lesson 11 of 20

The graph shows the distance travelled by a cyclist. (a) Calculate the speed in the first 20 s. (b) Describe the motion between 20 s and 40 s. (c) Calculate the speed between 40 s and 60 s. (4 marks)

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Question 1 · mark scheme

Forces

Lesson 11 of 20

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

5.0 m/s

1 mark

Stationary

1 mark

Correct distance and time

1 mark

3.0 m/s

1 mark

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Question 2 · 2 marks · State

Forces

Lesson 11 of 20

“

Describe what the gradient of a distance–time graph represents and what a horizontal line shows.

HOW TO ANSWER IT

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

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 2 · mark scheme

Forces

Lesson 11 of 20

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

Gradient is speed

1 mark

Horizontal line: stationary

1 mark

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 3 · 3 marks · Calculate

Forces

Lesson 11 of 20

“

A car travels 120 m in 10 s at constant speed. Sketch a distance–time graph for this and calculate the gradient.

HOW TO ANSWER IT

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

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 3 · mark scheme

Forces

Lesson 11 of 20

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

Straight line from the origin

1 mark

Correct end point

1 mark

12 m/s

1 mark

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Question 4 · 2 marks · Explain

Forces

Lesson 11 of 20

“

The distance–time graph for a runner is a curve that gets steeper. Describe the motion.

HOW TO ANSWER IT

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

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 4 · mark scheme

Forces

Lesson 11 of 20

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

Accelerating

1 mark

Gradient or speed increases

1 mark

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 5 · 3 marks · Determine

Forces

Lesson 11 of 20

“

The graph shows the distance of a car from a starting point against time as a curve. Describe how to find the speed at a particular time.

HOW TO ANSWER IT

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

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AQA GCSE PHYSICS · PAPER 2 · FOUNDATION & HIGHER

Question 5 · mark scheme

Forces

Lesson 11 of 20

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

Draw a tangent

1 mark

Choose two points on the tangent

1 mark

Gradient = change in distance ÷ change in time

1 mark

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