Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A lorry with mass $15\,000\,\text{kg}$ travels along a straight horizontal road from $A$ to $B$. Its speed is $20\,\text{m s}^{-1}$ at $A$ and $25\,\text{m s}^{-1}$ at $B$. The engine power of the lorry is constant, and the resistance to motion has constant magnitude $6000\,\text{N}$. The acceleration of the lorry at $B$ is $0.5$ times the acceleration of the lorry at $A$.
(a)[5]
Show that the power of the lorry’s engine is $200\,\text{kW}$, and hence find the acceleration of the lorry as it travels at $20\,\text{m s}^{-1}$.
(b)[2]
The lorry starts to climb a straight hill inclined at $1^\circ$ to the horizontal. It is stated that both the lorry’s engine power and the resistance force stay unchanged. Find the steady speed up the hill that the lorry could maintain.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Application of $P=Fv$” …