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 · View as Markdown

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

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.

Model answer (4 marks)

The stopping distance is determined by the work done by the braking force. The work done equals the braking force multiplied by the stopping distance, and this work must equal the loss of kinetic energy of the vehicle. The initial kinetic energy is ½mv². If the speed is doubled to 2v, the kinetic energy becomes ½m(2v)² = 2² × ½mv² = 4 × ½mv², i.e. four times larger. Because the braking force is unchanged, the work required to stop the vehicle is four times larger, so the stopping distance must also be four times larger. Thus the stopping distance at 2v is more than twice the stopping distance at v.

Examiner tips

  • Show the work–energy relation first, then link to kinetic energy, then to stopping distance.
  • Use the formula Ek = ½mv² and state the factor of 4 clearly.
  • Mention that the force is the same in both cases to justify proportionality.

Common mistakes

  • Confusing stopping distance with stopping time; forgetting the work–energy principle.
  • Using the wrong kinetic energy formula or mis‑calculating the factor of 4.
  • Assuming the stopping distance is exactly twice without explaining the energy argument.

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 in this question

stopping distance · braking force

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