Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A lorry with mass $24\,000\,\text{kg}$ is moving uphill on a slope that makes an angle of $3^\circ$ with the horizontal. The engine produces constant power, and the resistive force opposing the motion is constant at $3200\,\text{N}$.
(i)[4]
At a speed of $25\,\text{m s}^{-1}$, the lorry’s acceleration is $0.2\,\text{m s}^{-2}$. Calculate the power developed by the lorry’s engine.
(ii)[2]
Calculate the steady speed at which the lorry travels up the hill if the power is $500\,\text{kW}$ and the resistance stays at $3200\,\text{N}$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use Newton’s second law along the hill, for example $F - 24000\sin3 - 3200 = 24000 \times 0.2$” …