Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A car with mass $1400\,\text{kg}$ moving at speed $v\,\text{m}\,\text{s}^{-1}$ is subject to a resistive force of magnitude $40v\,\text{N}$. On a straight level road, the car’s highest possible constant speed is $56\,\text{m}\,\text{s}^{-1}$.
(i)[2]
Find, in $\text{kW}$, the largest possible power of the car’s engine.
(ii)[3]
Find the greatest possible acceleration of the car at the moment when its speed on a straight level road is $32\,\text{m}\,\text{s}^{-1}$.
(iii)[4]
The car moves down a hill inclined at an angle of $\theta^\circ$ to the horizontal with a constant speed of $50\text{ m s}^{-1}$. The engine power is $60\text{ kW}$. Find the value of $\theta$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set $\dfrac{\text{Power}}{\text{Velocity}}$ equal to the resistance, for example $\dfrac{P}{56} = 40\times56$” …