Free GCSE Physics lesson: Motion Graphs
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Free Lessons -> GCSE / Key Stage 4 -> Physics -> Motion Graphs

Lesson 14 · GCSE / Key Stage 4 · Physics

Distance-time and velocity-time graphs

Read motion graphs, calculate gradients and use area under velocity-time graphs.

Qualification: GCSE Subject: Physics Graphs Separate Physics and Combined Science

Forces

This lesson builds distance-time and velocity-time graphs for GCSE Physics.

Use the core lesson first, then match the exam-board guidance to your school route. Many pupils meet this content through Combined Science as well as Separate Physics.

Good forSeparate Physics and Combined Science
FocusDistance-time and velocity-time graphs
Time45-60 minutes
EquipmentRuler, calculator and graph paper.
Paper fitPaper 2 focus on most GCSE Physics routes
TierFoundation core with Higher stretch
Practical linkNo required practical focus
Maths tagsM1 substitution with units, M2 rearranging/equations, M4 graph gradients

What you will learn

  • Interpret horizontal and sloping sections on distance-time graphs.
  • Calculate speed from the gradient of a distance-time graph.
  • Interpret acceleration from a velocity-time graph.
  • Calculate distance from the area under a velocity-time graph.

Exam-board fit

RouteSeparate Physics and Combined Science
PaperPaper 2 focus on most GCSE Physics routes
TierFoundation core with Higher stretch
Specification fitForces: Distance-time and velocity-time graphs
Practical linkNo required practical focus
Maths ladderM1 substitution with units, M2 rearranging/equations, M4 graph gradients

Exact paper labels and specification-point numbering vary by board and cohort, so match this lesson to your school route before using past-paper questions.

Graph descriptions supplied on this page

Use the journey and trolley graph descriptions to practise gradient, area and motion language.

Clear explanation

On a distance-time graph, gradient represents speed. A steeper line means a greater speed; a horizontal line means stationary.

On a velocity-time graph, gradient represents acceleration. The area under the graph represents distance travelled.

Graph questions reward method: mark two clear points for gradient and split areas into rectangles and triangles when needed.

Key graph

Distance-time graph gradient A straight distance-time graph rises from zero metres at zero seconds to forty metres at eight seconds, so the gradient is speed. time / s distance / m 8 s 40 m gradient = speed
Graph: speed is found from change in distance divided by change in time.
Velocity-time graph area A velocity-time graph has a horizontal line at twelve metres per second from zero to five seconds, making a rectangle whose area represents distance. time / s velocity / m/s area = distance 12 m/s 5 s
Graph: area under a velocity-time graph gives distance travelled.

Worked examples

Distance from a velocity-time graph

A car travels at 12 m/s for 5 s.

distance = area under velocity-time graph

area = 12 x 5 = 60

Answer: The car travels 60 m.

Quick checks

Choose an answer, then check your thinking.

1. What does the gradient of a distance-time graph represent?

2. What does the area under a velocity-time graph represent?

Practice questions

Question 1

A distance-time graph rises from 0 m to 40 m in 8 s. Calculate speed.

Reveal answer and marking guidance

Answer: 5 m/s.

Marking: Credit gradient = 40 ÷ 8 = 5 m/s.

Question 2

A velocity-time graph is horizontal at 6 m/s for 10 s. Calculate distance.

Reveal answer and marking guidance

Answer: 60 m.

Marking: Credit area = 6 x 10 = 60 m.

Question 3

A velocity changes from 2 m/s to 14 m/s in 6 s. Calculate acceleration.

Reveal answer and marking guidance

Answer: 2 m/s².

Marking: Credit gradient = change in velocity ÷ time = 12 ÷ 6 = 2 m/s².

Question 4

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

Reveal answer and marking guidance

Answer: The object is stationary.

Marking: Credit distance not changing as time passes.

Exam practice ladder

AO1 fluencyRecall the key definition, unit, equation or model before using the lesson questions.
AO2 applicationApply distance-time and velocity-time graphs to an unfamiliar device, practical setup or data description.
AO3 analysisUse evidence, graph features, uncertainty, method quality or conclusion wording where the question asks you to evaluate.
Maths skillM1 substitution with units

Answers and marking guidance

The exact practice answers are hidden under each question so you can try first. For this lesson, marks come from using the correct physics model, choosing the right equation where needed, keeping units with values, and explaining changes with precise words such as transfer, resultant force, acceleration, evidence and uncertainty.

Common mistakes

  • Confusing distance-time and velocity-time gradients.
  • Using the whole graph as one shape when it needs splitting.
  • Calling a flat distance-time graph constant speed.
  • Forgetting graph units.

Exam-board guidance

All supported routes assess the core physics idea, but they may group topics, practicals and paper wording differently.

AQA GCSE Physics

AQA GCSE Physics: use this lesson for distance-time and velocity-time graphs, then check whether your class is taking Separate Physics or Combined Science.

OCR GCSE Physics

OCR GCSE Physics: the core physics idea is shared, but Gateway and Twenty First Century may organise questions differently.

Pearson Edexcel GCSE Physics

Pearson Edexcel GCSE Physics: practise the concept, the equation use and the practical language because questions often connect them.

Eduqas GCSE Physics

Eduqas GCSE Physics: learn the core explanation and practise applying it to unfamiliar contexts, data and practical questions.

WJEC Wales

WJEC Wales: check whether your class is using the current GCSE Physics route or a newer science route, then use this lesson for the shared physics idea.

CCEA GCSE Physics

CCEA GCSE Physics: connect the idea to your unit and remember that practical skills are assessed directly.

Extension challenge

Sketch a velocity-time graph with acceleration, steady speed and deceleration, then calculate a possible total distance.

Reveal answer

Example answer: A strong extension response names the physics model, uses accurate units and explains why the evidence supports the conclusion.

Next lesson

Next, continue with Newton's Laws and Resultant Forces.

Previous lesson: Heating CalculationsBack to GCSE Physics lessonsNext lesson: Newton's Laws and Resultant Forces