# 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.

> IB DP Physics Standard Level (2023 syllabus) — A.1 Kinematics · Explain · 4 marks

## Mark scheme (4 marks)

1. Uniform acceleration means velocity increases at a constant rate over time
2. Displacement is determined by the area under the velocity–time graph, which is triangular (or equivalent: displacement equals the average velocity multiplied by time)
3. Because velocity itself increases with time, the displacement accumulated in each successive time interval is greater than in the previous one
4. 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

- [uniform acceleration](https://www.gradenine.co.uk/glossary/uniform-acceleration)
- [displacement](https://www.gradenine.co.uk/glossary/displacement)
- [directly proportional](https://www.gradenine.co.uk/glossary/directly-proportional)

## Related

- [Revision notes for IB DP Physics Standard Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-the-displacement-of-an-ee465c9e) · Published by Druglandscape Ltd.