(i)[2]
Show that $\frac{9}{15 - v} \frac{dv}{dt} = 1$;
(ii)[4]
Solve this differential equation to show that $v = 15(1 - e^{-t/9})$;
(iii)[4]
Find the distance travelled by the cyclist in the first $9\,\text{s}$ of the motion:
Mathematics 9709 · AS & A Level · Probability
Probability — practice question
A cyclist and a bicycle together have mass $81\,\text{kg}$. He begins from rest and travels in 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 $v\,\text{m s}^{-1}$ denotes the cyclist’s speed at time $t$ s after starting.