A train travels along a straight track between two stations. For the first part of the journey, the train accelerates uniformly from rest. It then travels at a constant velocity. Finally, it decelerates uniformly to rest at the second station. Describe what a velocity-time graph of this entire journey would look like, and state what feature of the graph could be used to find the total distance travelled between the two stations.

Pearson Edexcel International GCSE Physics (4PH1) — 1.2 Movement and position · Describe · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

A train starts from rest at one station and comes to rest at the next station along a straight track.

Model answer (4 marks)

The graph starts at the origin (0 s, 0 m s⁻¹) and rises linearly with a positive slope, showing uniform acceleration from rest. It then becomes a horizontal straight line, indicating the train moves at a constant velocity. Finally, the line slopes downwards with a negative gradient, returning to the origin, representing uniform deceleration to rest. The total distance travelled is given by the area under the whole velocity‑time curve.

Examiner tips

  • Use the correct axes: time on x‑axis, velocity on y‑axis. Show the three distinct straight‑line sections. Mention that the area under the curve equals distance. Keep the description concise and use terms like ‘positive gradient’ and ‘horizontal line’.
  • Remember the graph must start and end at zero velocity – this shows the train starts and stops. The constant‑velocity section should be a flat line, not a slanted one.

Mark scheme (4 marks)

  1. The graph starts at zero velocity and shows a straight line with a positive gradient (uniform acceleration from rest).
  2. The graph then shows a horizontal straight line, indicating constant / steady velocity.
  3. The graph ends with a straight line with a negative gradient (uniform deceleration) back down to zero velocity.
  4. The total distance travelled is found from the area under the velocity-time graph.

Key terms in this question

velocity-time graph · constant velocity · distance

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