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4MA1/1HR Jun 2019, Question 16: The Second Derivative

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks

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The question, in short

Particle P moves on a line through fixed point O with displacement s = 4t³ − 6t² + 5t metres at time t seconds. Find velocity expression and when acceleration equals 6 m/s².

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Part (a) · 2 marks

Find an expression for the velocity v in terms of t from the given displacement s.

  1. 1Velocity is the derivative of displacement: v = ds/dt
  2. 2Differentiate each term: 4t³ → 12t², −6t² → −12t, 5t → 5
  3. 3v = 12t² − 12t + 5

Answer12t² − 12t + 5

Part (b) · 3 marks

Find the time t at which the acceleration of P is 6 m/s².

  1. 1Acceleration is the derivative of velocity: a = dv/dt
  2. 2v = 12t² − 12t + 5, so a = 24t − 12
  3. 324t − 12 = 6, so 24t = 18
  4. 4t = 18 ÷ 24 = 0.75

Answer0.75

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