Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A cyclist moves along a straight level road. She is producing power at a steady rate of $150\,\text{W}$. At the instant when her speed is $4\,\text{m s}^{-1}$, her acceleration is $0.25\,\text{m s}^{-2}$. The resistance opposing motion is $20\,\text{N}$.
(a)[3]
Calculate the combined mass of the cyclist and her bicycle.
(b)[2]
The cyclist reaches a straight hill inclined at an angle $\theta$ above the horizontal. She climbs the hill at constant speed $3\,\text{m s}^{-1}$. She keeps working at the same rate as before and the resistance force is unchanged. Find the value of $\theta$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Forward force obtained from $P = Fv$, giving $F = \frac{150}{4} = 37.5\,\text{N}$” …