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 · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

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

Model answer (4 marks)

1. On a steeper gradient the component of the car’s weight acting down the road increases.
2. To keep the speed constant the engine must supply a driving force that balances this larger resistive force, so the driving force must increase.
3. Power is the rate of doing work, P = Fv; with speed v fixed, a larger driving force means a larger power output.
4. The engine also has to raise the car’s gravitational potential energy per unit time, which is the extra work required on the steeper slope.

Examiner tips

  • Use the formula P = Fv and state that v is constant; emphasise the increase in resistive force due to gravity.
  • Show the chain of reasoning: steeper slope → larger opposing force → larger driving force → larger power.
  • Mention the work against gravity as part of the power requirement.

Common mistakes

  • Confusing the engine’s power with the car’s kinetic energy; the car’s kinetic energy is constant at constant speed.
  • Failing to state that the resistive force increases because of the steeper gradient.
  • Using the wrong sign for the gravitational component or omitting the work against gravity.

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 in this question

power · gradient · constant speed

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