Explain why the displacement of an object undergoing uniform acceleration is not directly proportional to the time elapsed, even when the object starts from rest.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Model answer (4 marks)
Uniform acceleration means the velocity increases at a constant rate, so v(t)=at.
The displacement is the area under the v–t graph; for a straight‑line graph this area is a triangle, giving s=½at².
Because the velocity itself grows with time, each successive time interval contributes more displacement than the previous one.
Thus s is proportional to t², not to t, so the displacement is not directly proportional to the elapsed time.
The displacement is the area under the v–t graph; for a straight‑line graph this area is a triangle, giving s=½at².
Because the velocity itself grows with time, each successive time interval contributes more displacement than the previous one.
Thus s is proportional to t², not to t, so the displacement is not directly proportional to the elapsed time.
Examiner tips
- Show the v–t graph or the equation s=½at²; this demonstrates the t² dependence.
- Explain that the area under the graph is triangular, not rectangular.
- Highlight that velocity increases, so later intervals add more distance.
- Use the phrase "not directly proportional" to match the mark scheme.
Common mistakes
- Using s=at instead of s=½at², implying linearity.
- Forgetting to mention the triangular area or the average velocity concept.
- Not recognising that the relationship is quadratic, not linear.
Mark scheme (4 marks)
- Uniform acceleration means velocity increases at a constant rate over time
- Displacement is determined by the area under the velocity–time graph, which is triangular (or equivalent: displacement equals the average velocity multiplied by time)
- Because velocity itself increases with time, the displacement accumulated in each successive time interval is greater than in the previous one
- Therefore displacement is proportional to the square of the time (s ∝ t²), not to t, so the relationship is non-linear / not directly proportional
Key terms in this question
uniform acceleration · displacement · directly proportional
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
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