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2 marksApplications of Integration

CSEC Additional Mathematics · 2013 · Paper 2 · Question 8(a)(ii)b)

A particle starts from rest and accelerates uniformly to 20 m s⁻¹ in 5 seconds. It continues at this velocity for 10 seconds. It then accelerates again uniformly to a velocity of 60 m s⁻¹ in 5 seconds. The particle then decelerates uniformly until it comes to rest, 15 seconds later.

From your graph determine the average velocity of the particle for the entire journey.

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Other parts of this question

  1. 8(a)(i)On the graph paper provided, draw a velocity-time graph to illustrate the motion of the particle.[3 marks]
  2. 8(a)(ii)a)From your graph determine the total distance, in metres, travelled by the particle.[4 marks]
  3. 8(b)(i)Calculate the values of t when the particle is instantaneously at rest.[3 marks]
  4. 8(b)(ii)Calculate the distance travelled by the particle between 1 second and 3 seconds.[3 marks]
  5. 8(b)(iii)a)Calculate the value of dv/dt when t = 2 seconds.[2 marks]
  6. 8(b)(iii)b)Calculate the value of dv/dt when t = 3 seconds.[1 mark]
  7. 8(b)(iv)a)Give an interpretation for the value in 8(b)(iii)a).[1 mark]
  8. 8(b)(iv)b)Give an interpretation for the value in 8(b)(iii)b).[1 mark]

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