Distance–time graphs
Objective. Interpret gradient and sections of journey graphs.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
A distance–time graph plots how far an object has travelled against the time elapsed, with the gradient of each section representing the object's speed. A steeper line means a faster speed, a flat horizontal section means the object is stationary, and a line sloping back towards the time axis represents a return journey. To calculate speed from a section of the graph, divide the change in distance by the change in time for that section, just as with any straight-line gradient. For example, if a graph shows 20 km covered in 2 hours on one section, the speed during that section is 20 ÷ 2 = 10 km/h.
Worked example
A distance–time graph shows a cyclist travelling 15 km in the first hour, then resting, then travelling a further 10 km in the next half hour. Find the cyclist's speed during the second moving section.
- 1Identify the relevant section: 10 km covered in 0.5 hours.
- 2Speed is calculated as distance ÷ time.
- 3Substitute the values: 10 ÷ 0.5.
- 410 ÷ 0.5 = 20 km/h.
Answer: 20 km/h
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils often think a horizontal section of a distance–time graph means the object is moving at a constant slow speed, rather than realising it means the object has stopped completely. A flat section always represents zero speed, not slow movement.
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