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4024/12 May/Jun 2025, Question 18: Speed-Time Graphs and Acceleration

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 for a cyclist, describe one stage of motion, show that v = 10 from the given acceleration, and find T from a total distance of 1.4 km.

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

Part (a) · 1 mark

Describe how the cyclist's speed behaves between t = 40 and t = 100.

  1. 1The graph is horizontal: constant speed (v m/s)

AnswerConstant speed

Part (b) · 1 mark

Given acceleration 0.25 m/s² from t = 0 to t = 40, show that v = 10.

  1. 1v = acceleration × time = 0.25 × 40 = 10

Answer0.25 × 40 = 10

Part (c) · 3 marks

Given total distance 1.4 km from t = 0 to t = T, find the value of T.

  1. 1Distance = area under graph = 1/2 × (60 + T) × 10
  2. 25(T + 60) = 1400
  3. 3T + 60 = 280, so T = 220

Answer220

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