Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A cyclist together with his bicycle has a combined mass of $90\,\text{kg}$. He begins moving at a speed of $3\,\text{m s}^{-1}$ from the summit of a straight hill, with length $500\,\text{m}$, that is inclined at an angle of $\sin^{-1} 0.05$ to the horizontal. He travels with constant acceleration and arrives at the bottom of the hill at a speed of $5\,\text{m s}^{-1}$. While going downhill, the cyclist produces $420\,\text{W}$ of power. The resistive force on the cyclist and his bicycle, $R\,\text{N}$, and the cyclist’s speed, $v\,\text{m s}^{-1}$, both change.
(i)[5]
Show that $R = \frac{420}{v} + 43.56$
(ii)[3]
Find the cyclist’s speed at the midpoint of the hill. Hence determine the decrease in the value of $R$ as the cyclist travels from the top of the hill to the midpoint, and as the cyclist travels from the midpoint of the hill to the bottom.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Find the acceleration from $a=\dfrac{5^2-3^2}{2\times500}=0.016$” …