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4024/12 May/Jun 2020, Question 18: 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

Use a speed–time graph for a car, with top speed v reached at time T and held until 140 s, then falling to rest at 200 s, to find v and T.

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

Part (a) · 2 marks

Given deceleration 0.2 m/s² between t = 140 and t = 200, find the maximum speed v.

  1. 1Deceleration = v ÷ (200 − 140)
  2. 20.2 = v/60
  3. 3v = 0.2 × 60 = 12

Answer12

Part (b) · 3 marks

Given the car covers 1800 m in 200 s, find the time T at which speed v is first reached.

  1. 1Distance = area of trapezium = 1/2 × (200 + (140 − T)) × 12
  2. 21/2 × (340 − T) × 12 = 1800
  3. 36(340 − T) = 1800
  4. 4340 − T = 300
  5. 5T = 40

Answer40

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