# Explain why the power output of a car engine must increase if the car is to maintain a constant speed on a road with increasing gradient.

> IB DP Physics Higher Level (2023 syllabus) — A.3 Work, energy and power · Explain · 4 marks

> A car travels along a straight road. The road gradually becomes steeper whilst the car maintains a constant speed.

## Mark scheme (4 marks)

1. At constant speed on a steeper gradient, the component of gravitational force acting along the road (opposing motion) increases.
2. To maintain constant speed, the driving force must increase to balance the larger total resistive force (net force = zero).
3. Power is defined as the rate of doing work, or P = Fv, so for a given constant speed an increased driving force requires greater power.
4. On the steeper gradient the engine must also do work against gravity (increase the car's gravitational potential energy per unit time), which accounts for the additional power required.

## Key terms

- [power](https://www.gradenine.co.uk/glossary/power)
- [gradient](https://www.gradenine.co.uk/glossary/gradient)
- [constant speed](https://www.gradenine.co.uk/glossary/constant-speed)

## 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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