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4024/12 Oct/Nov 2021, Question 14: Area Under a Speed-Time Graph

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Using a speed-time graph of a cyclist over 50 seconds, work out acceleration, describe a section of motion, and calculate total distance.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (a) · 1 mark

Work out the acceleration for the first 20 seconds from the graph.

  1. 1Acceleration = gradient = 15/20 = 0.75 m/s²

Answer15/20

Part (b) · 1 mark

State how the cyclist moves from t = 20 to t = 30.

  1. 1The line is horizontal, so speed is constant (15 m/s)

AnswerSpeed is constant

Part (c) · 3 marks

Work out the overall distance covered across the full 50 seconds.

  1. 1Distance = area under graph
  2. 20 to 20 s: 1/2 × 20 × 15 = 150
  3. 320 to 30 s: 10 × 15 = 150
  4. 430 to 50 s: 1/2 × (15 + 5) × 20 = 200
  5. 5Total = 150 + 150 + 200 = 500 m

Answer500

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