(i)[2]
Show that this gives $\dfrac{9}{15 - v}\,\dfrac{dv}{dt} = 1$.
(ii)[4]
Solve this differential equation, and show that $v = 15(1 - e^{-t/9})$.
(iii)[4]
Determine how far the cyclist travels during the first $9\ \text{s}$ of the motion.
Mathematics 9709 · AS & A Level · Representation of data
Representation of data — practice question
A cyclist and his bicycle together have a mass of $81\ \text{kg}$. He begins from rest and moves along a straight line. The cyclist applies a steady force of $135\ \text{N}$, while the motion is opposed by a resistance of magnitude $9v\ \text{N}$, where $v\ \text{m s}^{-1}$ represents the cyclist's speed at time $t$ after starting.