A student wants to estimate the kinetic energy of a cyclist travelling along a flat road. Explain how the student could arrive at a reasonable estimate, giving a final value with a unit.

AQA A-Level Physics (7408) — 3.1.3 Estimation of Physical Quantities · Explain · 5 marks · View as Markdown

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

Model answer (5 marks)

A reasonable estimate of the mass of a cyclist including the bicycle is about 80 kg.
The speed of a cyclist on a flat road is roughly 10 m s⁻¹.
The kinetic energy is given by KE = ½mv².
Substituting the estimates gives KE = ½ × 80 kg × (10 m s⁻¹)² = ½ × 80 × 100 = 4000 J.
Therefore the kinetic energy is about 4 × 10³ J.

Examiner tips

  • Use realistic ranges for mass (70–100 kg) and speed (5–15 m s⁻¹) to show you can estimate.
  • Write the equation KE = ½mv² before substitution.
  • Show the substitution step and keep units consistent.
  • Give the final answer in joules, using appropriate significant figures.

Mark scheme (5 marks)

  1. Recall or estimate the mass of a cyclist (including the bicycle) in a reasonable range, e.g. 70–100 kg
  2. Recall or estimate the speed of a cyclist in a reasonable range, e.g. 5–15 m/s (or converts a reasonable mph value correctly)
  3. States the equation for kinetic energy: KE = ½mv²
  4. Substitutes their estimated values correctly into the equation
  5. Gives a final answer consistent with their values and in joules (J)

Key terms in this question

kinetic energy · estimate

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