A hot-air balloon rises vertically from rest. For the first part of its ascent it accelerates upwards, then it travels at a steady velocity, and finally it decelerates to rest at a higher altitude. Describe what a velocity-time graph of the entire journey would look like, and state what feature of the graph could be used to find the total distance travelled.

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 hot-air balloon rises vertically from rest, accelerates upwards, then travels at a steady velocity, and finally decelerates to rest at a higher altitude.

Model answer (4 marks)

The graph starts at the origin (0,0). For the first part it rises with a positive slope, showing increasing velocity. Next it becomes a horizontal straight line, indicating constant velocity. Finally it slopes downwards to meet the time‑axis again, showing decreasing velocity to zero. The total distance travelled can be found from the area under the whole curve.

Examiner tips

  • Use a clear, continuous line for each phase
  • Show the origin and zero‑velocity points
  • State that the area under the curve gives distance
  • Mention that the slope represents acceleration

Common mistakes

  • Drawing a negative slope for the acceleration phase
  • Forgetting that the horizontal section is at a constant non‑zero velocity
  • Claiming the area gives time instead of distance

Mark scheme (4 marks)

  1. The graph starts at the origin (velocity = 0 at time = 0) and the line rises with a positive gradient during the acceleration phase.
  2. The line becomes horizontal (constant/zero gradient) during the steady velocity phase.
  3. The line then falls with a negative gradient back to zero velocity during the deceleration phase.
  4. The total distance travelled is found from the area under the velocity-time graph.

Key terms in this question

velocity-time graph · steady velocity · distance

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