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0606/11 Oct/Nov 2025, Question 9: Motion with Calculus

Cambridge IGCSE Additional Mathematics 0606 · Paper 11 (Non-calculator) · Non-calculator · 3 marks

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The question, in short

From a velocity–time graph of a particle on a straight line, draw the matching speed–time graph, then use the given quadratic form with zero gradient at time 0 to draw a possible acceleration–time graph.

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

Part (a) · 1 mark

Sketch speed against time on the blank axes, using the given velocity–time curve from time 0 to 3.

  1. 1Speed = |velocity|
  2. 2Reflect the part of the curve below the time axis in the time axis
  3. 3The part above the axis is unchanged

AnswerThe same curve as the velocity–time graph but with the negative part reflected in the time axis (positive at time 0, decreasing to 0 where the velocity crosses the axis, then increasing)

Part (b) · 2 marks

Using the quadratic velocity curve with zero gradient at time 0, sketch a possible acceleration–time graph on the blank axes.

  1. 1v is quadratic in t with gradient 0 at t = 0, so v = pt² + q with p > 0
  2. 2a = dv/dt = 2pt
  3. 3So a is a straight line through O with positive gradient

AnswerA straight line through the origin with positive gradient

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