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3 marksKinematics and Dynamics

CAPE Applied Mathematics Unit 2 · 2013 · Paper 2 · Question 5(c)(ii)

A cyclist climbing a hill starts at 10\text{ ms}^{-1} with velocity modelled by \frac{\mathrm{d}x}{\mathrm{d}t} = 10 - kx, where 10 - kx > 0.

On reaching the top of the 75 m long hill, his velocity has dropped to 4\text{ ms}^{-1}. Find the value of k.

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Other parts of this question

  1. 5(a)(i)Draw a diagram to illustrate this information, and hence draw the coplanar force diagram.[5 marks]
  2. 5(a)(ii)Calculate the tension in the string.[2 marks]
  3. 5(b)Calculate the frictional resistance of the railway.[8 marks]
  4. 5(c)(i)Show that t = \frac{1}{k}\ln\left(\frac{10}{10 - kx}\right).[7 marks]

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