Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A cyclist is travelling uphill on a straight slope that makes an angle $\alpha$ with the horizontal, with $\sin \alpha = 0.04$. The combined mass of the bicycle and rider is $80\,\text{kg}$. The cyclist maintains a constant speed of $4\,\text{m s}^{-1}$. A resistive force acts against the motion. The work completed by the cyclist against this resistive force over $25\,\text{m}$ is $600\,\text{J}$.
(i)[4]
Determine the cyclist's power output.
(ii)[4]
When the cyclist reaches the top of the hill and the road levels off, the speed is $4\,\text{m s}^{-1}$. The cyclist keeps producing the same power on the horizontal section. Determine the speed of the cyclist $10\,\text{s}$ after reaching the top of the hill, given that the work done by the cyclist in this interval against the resistance force is $1200\,\text{J}$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Resistance force correctly found: $\frac{600}{25} = 24\,\text{N}$” …