Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A cyclist is moving along a straight horizontal road. The combined mass of the cyclist and his bicycle is $80\,\text{kg}$. His power output stays constant at $240\,\text{W}$. When his speed is $6\,\text{m s}^{-1}$, his acceleration is $0.3\,\text{m s}^{-2}$.
(i)[3]
Show that the force resisting the cyclist’s motion is $16\,\text{N}$.
(ii)[2]
Find the steady speed the cyclist can keep if both his power output and the resistance force stay unchanged.
(iii)[3]
The cyclist then rides up a straight hill inclined at $3^\circ$ to the horizontal. His power output and the resistance force remain unchanged. Find his acceleration when he is travelling at $4\,\text{m s}^{-1}$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies the power relation $P=Fv$ to obtain the driving force $=\tfrac{240}{6}=40\,\text{N}$” …