Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A cyclist travels on a horizontal straight road with a constant power output of $160\,\text{W}$. The resistive force opposing the motion is constant at $20\,\text{N}$. At the moment when the cyclist’s speed is $5\,\text{m s}^{-1}$, the acceleration is $0.15\,\text{m s}^{-2}$.
(i)[3]
Show that the combined mass of the cyclist and bicycle is $80\,\text{kg}$.
(ii)[2]
The cyclist reaches a hill inclined at $2^\circ$ to the horizontal. As he begins to climb, he increases his power to a constant $300\,\text{W}$. The resistance to motion stays at $20\,\text{N}$. Show that the steady speed up the hill that the cyclist can keep at this power is $6.26\,\text{m s}^{-1}$, correct to $3$ significant figures.
(iii)[4]
Find the acceleration at an instant when the cyclist is travelling at $90\%$ of the speed in part (ii).
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Driving force from power $= \frac{160}{5} = 32\text{ N}$.” …