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0606/22 May/Jun 2026, Question 9: Motion with Calculus

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

Particle P moves with displacement s = e^(4t) − 10e^(2t) + 9 metres from fixed point O. Find the time when velocity is stationary, and the acceleration at t = ln 2.

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Part (a) · 5 marks

Differentiate s to get velocity v, then find the value of t where v has a stationary value.

  1. 1v = ds/dt = 4e^(4t) − 20e^(2t)
  2. 2dv/dt = 16e^(4t) − 40e^(2t)
  3. 3dv/dt = 0: 8e^(2t)(2e^(2t) − 5) = 0
  4. 4e^(2t) = 40/16 = 5/2
  5. 5t = (1/2) ln(5/2) = 0.458

Answert = (1/2) ln(5/2) (0.458)

Part (b) · 2 marks

Find the acceleration of P at the time t = ln 2.

  1. 1a = dv/dt = 16e^(4t) − 40e^(2t)
  2. 2At t = ln 2: e^(2t) = 4, e^(4t) = 16
  3. 3a = 16(16) − 40(4) = 256 − 160 = 96 m s⁻²

Answer96

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