7 marksKinematics and Dynamics
CAPE Applied Mathematics Unit 2 · 2013 · Paper 2 · Question 5(c)(i)
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.
Show that t = \frac{1}{k}\ln\left(\frac{10}{10 - kx}\right).
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