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4PM1/02R Jun 2019, Question 4: Motion with Calculus

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 8 marks

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The question, in short

Particle P on the x-axis has acceleration a = 6t − 12 m/s², starting from rest at the origin at t = 0. Find velocity at t = 2, the later time T when P is instantaneously at rest, and the distance travelled in the first 8 seconds.

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Part (a) · 3 marks

Find the velocity of P at t = 2 seconds, given it starts from rest at the origin.

  1. 1v = ∫ (6t − 12) dt = 3t² − 12t + c
  2. 2t = 0, v = 0 ⇒ c = 0
  3. 3t = 2: v = 3 × 4 − 24 = −12 m/s

Answer−12 m/s

Part (b) · 2 marks

Find the positive time T at which P is instantaneously at rest.

  1. 1v = 0: 3t² − 12t = 0
  2. 23t(t − 4) = 0
  3. 3T > 0 ⇒ T = 4

AnswerT = 4

Part (c) · 3 marks

Find the total distance travelled by P during the first 8 seconds of motion.

  1. 1s = ∫ (3t² − 12t) dt = t³ − 6t²
  2. 20 to 4: [t³ − 6t²] = −32, so 32 m
  3. 34 to 8: (512 − 384) − (64 − 96) = 160 m
  4. 4Distance = 32 + 160 = 192 m

Answer192 m

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