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Travel Graph Lab

Maths · Cambridge O Level · Travel graphs · Distance, speed and time

Build a three-stage journey. Watch a vehicle move, read distance–time gradients and calculate distance from speed–time areas.

Preview of Travel Graph Lab

Free to explore. The interactive lab loads only when you start. No account or saved progress.

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Things to try

  1. Play the initial journey. Explain why the distance graph is horizontal during Stage 2 while the vehicle remains still.
  2. Switch to Speed–time and show area shading. Calculate 4 × 10 + 0 × 5 + ½ × (2 + 6) × 10 = 80 m. Check the average speed, including the stop.
  3. Load Steady journey. Predict the shape of both graphs. Double one stage duration: which totals change and which speed stays the same?
  4. Load Accelerate then brake. Compare the curved distance graph with the sloping speed graph. Explain why a downward-sloping speed graph can still mean moving forward.
  5. Load Stay at rest. Then increase one stage’s start and end speeds. Use the time slider to compare the exact boundary speed and the continuous distance.

Key ideas

  • Speed is the gradient of a distance–time graph. A horizontal section means no distance is being added, so the vehicle is at rest.
  • On a speed–time graph, horizontal means constant speed; an upward or downward slope means acceleration or deceleration. Speed stays non-negative here.
  • Distance travelled equals the area under a speed–time graph. For a stage with linearly changing speed, distance = ½ × (starting speed + ending speed) × duration.
  • Average speed is total distance divided by total time, including stops. Playback speed is only a viewing control and does not change the journey measurements.
  • This forward-only, idealised model permits instantaneous speed changes between stages. The dashed jump is not a physically achievable finite acceleration. A completed observation need not end at rest.

Exam tip

Check the axis labels first. A flat distance–time graph means rest, but a flat speed–time graph can mean steady motion. Calculate graph areas with seconds and metres per second to obtain metres. Do not treat distance and displacement as interchangeable for a return journey.

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