# Explain why the stopping distance of a vehicle travelling at twice the speed is more than twice the stopping distance of the same vehicle travelling at the original speed, assuming the same braking force in both cases.

> IB DP Physics Higher Level (2023 syllabus) — A.2 Forces and momentum · Explain · 4 marks

> A vehicle brakes to a complete stop from an initial speed v. The same vehicle, under identical road and braking conditions, brakes to a complete stop from an initial speed 2v.

## Mark scheme (4 marks)

1. The braking force does work against the kinetic energy of the vehicle, so the stopping distance is determined by the initial kinetic energy.
2. Kinetic energy is proportional to the square of speed (Ek = ½mv²), so doubling the speed quadruples the kinetic energy.
3. Since the braking force is the same, the work done equals force multiplied by stopping distance, so stopping distance is proportional to kinetic energy.
4. Therefore the stopping distance at speed 2v is four times (not twice) the stopping distance at speed v, which is more than double.

## Key terms

- [stopping distance](https://www.gradenine.co.uk/glossary/stopping-distance)
- [braking force](https://www.gradenine.co.uk/glossary/braking-force)

## Related

- [Revision notes for IB DP Physics Higher 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-stopping-distance-of-52c27eb5) · Published by Druglandscape Ltd.