What mistakes do students make with The distance–time relationship?

Dividing a single pair of coordinates rather than using the changes. Using a small triangle, so that reading errors dominate the answer. Taking a gradient across a curved section as though it were straight.

What are the exam tips for The distance–time relationship in Physics AQA GCSE?

Draw the triangle on the graph itself; examiners give credit for the working shown there. Choose points where the line crosses grid lines exactly so the readings are easy.

AQA · GCSE · Physics

Course version: 8463 · Version from Sept 2016

The speed of an object can be calculated from the gradient of its…

Full specification wording

The distance–time relationship: The speed of an object can be calculated from the gradient of its distance–time graph.

Speed is distance divided by time, and that is exactly what a gradient is on this graph, so the two are the same calculation.

Checked against the AQA 8463 specification (opens in a new tab) on 22 September 2026.

Point 2 of 5

Study notes

From the checked teaching notes for this specification point.

The idea

What earns the marks

Reading a correct change in distance with the matching change in time.
A correct substitution into speed = change in distance divided by change in time.
The correctly calculated speed.
The unit that follows from the axes, converted where the question requires it.

Common mistakes and how to put them right

Dividing a single pair of coordinates rather than using the changes.
Using a small triangle, so that reading errors dominate the answer.
Taking a gradient across a curved section as though it were straight.
Ignoring an axis marked in kilometres or in minutes.

Exam tips

Draw the triangle on the graph itself; examiners give credit for the working shown there.
Choose points where the line crosses grid lines exactly so the readings are easy.

Try the lesson

The start of the The distance–time relationship: The speed of an object can be calculated from the gradient of its distance–time graph. lesson, made from checked teaching notes for this specification point.

Have a go first

What does the gradient of a distance–time graph represent?

Tip: press 1 to 4 to choose

Listen

Speed is distance divided by time, and that is exactly what a gradient is on this graph, so the two are the same calculation. Pick two points far apart on the straight section, because a large triangle reduces the effect of reading error, and take the change in distance together with the change in time between them. A telescope's graph showing 38 km covered in 5.0 s gives a speed of 7.6 km/s. Mark schemes award one mark for reading a correct pair of changes, one for the substitution and one for the answer, so show all three steps. Read the axis units before dividing, because a vertical axis in kilometres and a horizontal axis in seconds give an answer in kilometres per second unless you convert first. A strong answer earns marks for these points. reading a correct change in distance with the matching change in time. a correct substitution into speed = change in distance divided by change in time. the correctly calculated speed. the unit that follows from the axes, converted where the question requires it. Exam tip: Draw the triangle on the graph itself; examiners give credit for the working shown there.

See it

A top-down flowchart. The first box says to pick two points far apart on the straight section. Two arrows lead from it to two boxes: one to read the change in distance between them, and one to read the matching change in time between them. Both of these boxes lead into a box saying to substitute into speed = change in distance divided by change in time. That box leads to a box saying to calculate the speed, which leads to a final box saying to give the unit that follows from the axes, converted where required. — The steps for calculating a speed from the gradient of a straight section of a distance–time graph, from choosing widely separated points to giving the unit.

Label the diagram

Some boxes have lost their names. Pick the right name for each number.

The diagram again, with 3 boxes numbered instead of named. A top-down flowchart. The first box says to pick two points far apart on the straight section. Two arrows lead from it to two boxes: one to read the change in distance between them, and one to read the matching change in time between them. Both of these boxes lead into a box saying to substitute into speed = change in distance divided by change in time. That box leads to a box saying to calculate the speed, which leads to a final box saying to give the unit that follows from the axes, converted where required.

1Box 1
2Box 2
3Box 3

0 of 3 labelled

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