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0580/42 Feb/Mar 2025, Question 16: Area Under a Speed-Time Graph

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 6 marks

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The question, in short

From a speed-time graph of a 30-second cyclist journey, find accelerations and an average speed using the curve, flat section and final descent.

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

Part (a) · 1 mark

State the acceleration between 15 s and 25 s from the horizontal part of the graph.

  1. 1Speed is constant at 8 m/s, so acceleration = 0 m/s²

Answer0

Part (b) · 2 marks

Estimate the acceleration at 7.5 s by drawing a tangent to the curve.

  1. 1Draw a tangent touching the curve at (7.5, 7), e.g. through (0, 4.5) and (15, 9.5)
  2. 2Gradient = (9.5 − 4.5)/(15 − 0) = 5/15
  3. 3≈ 0.33 m/s²

Answer0.25 to 0.4

Part (c) · 3 marks

Calculate the average speed between 15 s and 30 s.

  1. 1Distance = area under graph from 15 s to 30 s
  2. 2= 10 × 8 + 1/2 × 5 × 8 = 80 + 20 = 100 m
  3. 3Average speed = 100 ÷ 15 = 6.666… ≈ 6.67 m/s

Answer6.666 to 6.733…

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