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Travel Graphs

FoundationHigherAQAEdexcelOCR

This free Foundation and Higher GCSE Maths worksheet on travel graphs helps you revise interpreting distance-time and travel graphs. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. On a distance-time graph the gradient is the speed; a flat line means stationary.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

WorksheetFoundation · PDFMark SchemeFoundation · PDF

Higher

WorksheetHigher · PDFMark SchemeHigher · PDF

Topic overview

A travel graph, also called a distance-time graph, shows how far something has travelled over time. Distance is on the vertical axis and time on the horizontal.

The gradient of the line is the speed, because it is distance divided by time. A steeper line therefore means faster travel, and a horizontal line means the object is stationary.

A line returning to the horizontal axis shows the journey coming back to the starting point. The total distance travelled is then more than the final displacement, which is a distinction some questions deliberately test.

Revision notes

Reading speed from the gradient

Speed equals distance divided by time, which is exactly the gradient of the line.

A line rising \(60\) km over \(2\) hours has a gradient of \(30\), so the speed is \(30\) km per hour. Always give the units.

Horizontal sections

A horizontal line means distance is not changing, so the object is stationary.

The length of the horizontal section tells you how long the stop lasted. Time still passes, but no distance is covered.

Return journeys

A line sloping back down towards the time axis shows travel back towards the start.

The steeper the return, the faster the journey home. When the line reaches the axis, the object is back where it began.

Key points

  • Distance is on the vertical axis, time on the horizontal.
  • The gradient gives the speed.
  • A steeper line means a faster speed.
  • A horizontal line means the object is stationary.
  • A downward slope means returning towards the start.
  • Always give speed with units.

Worked examples

Example 1

A cyclist travels \(45\) km in \(3\) hours. Find the speed from the graph.

Working

\[45 \div 3\]the gradient is distance divided by time
\[= 15 \text{ km/h}\]state the speed with units

Example 2

A travel graph has a horizontal section lasting \(30\) minutes. Describe what happens.

Working

\[\text{Distance does not change}\]a horizontal line means no movement
\[\text{The object is stationary for 30 minutes}\]interpret in context

Example 3

A walker covers \(6\) km in \(90\) minutes. Find the speed in km/h.

Working

\[90 \text{ minutes} = 1.5 \text{ hours}\]convert the time to hours
\[6 \div 1.5\]divide distance by time
\[= 4 \text{ km/h}\]state the speed with units

Common mistakes

  • Reading a horizontal line as constant speed.

    A horizontal line means the object has stopped, since distance is not changing.

  • Forgetting to convert minutes to hours.

    For km/h the time must be in hours, so 90 minutes is 1.5.

  • Confusing steepness with distance.

    A steeper line means a greater speed, not a greater distance.

  • Omitting units from the speed.

    The answer needs km/h or m/s, not just a number.

Exam tips

  • Convert all times to the unit required by the answer.
  • Describe each section of the journey separately.
  • Use a right-angled triangle to read the gradient accurately.
  • Always include units when giving a speed.

Key terms

Distance-time graph
A graph showing distance travelled against time.
Speed
Distance travelled per unit of time, given by the gradient.
Stationary
Not moving, shown by a horizontal line.
Gradient
The steepness of a line, here representing speed.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.