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4 marksKinematics and Dynamics

CAPE Applied Mathematics Unit 2 · 2015 · Paper 2 · Question 5(c)

A particle of mass m falls vertically from rest through a medium with resistance to motion proportional to v, where v is its velocity at time t. Obtain a differential equation relating v and t.

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  1. 5(a)(i)Draw a force diagram to illustrate this information.[3 marks]
  2. 5(a)(ii)The particle is released from rest. Determine the tension, T, in the string and the acceleration, a, of the particle.[8 marks]
  3. 5(a)(iii)Calculate the force exerted by the string on the pulley.[4 marks]
  4. 5(b)(i)Find in vector form the acceleration when t = 3.[2 marks]
  5. 5(b)(ii)Find in vector form the position of the particle when t = 3.[4 marks]

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