Mathematics 9709 · AS & A Level · Energy, work and power
Energy, work and power — practice question
A car with mass $1600\ \text{kg}$ is towing a caravan with mass $800\ \text{kg}$. A light rigid tow-bar joins the car to the caravan. The resistances to the motion of the car and caravan are $400\ \text{N}$ and $250\ \text{N}$ respectively.
(a(i))[2]
With the car and caravan moving at a constant speed of $25\ \text{m s}^{-1}$, find the power output of the car’s engine.
(a(ii))[5]
The engine’s power is now abruptly raised to $39\ \text{kW}$. Find the instantaneous acceleration of the car and caravan and the tension in the tow-bar.
(b)[3]
The car and caravan now move up a straight hill inclined at an angle of $\sin^{-1} 0.05$ to the horizontal, at constant speed $v\ \text{m s}^{-1}$. The car’s engine is operating at $32.5\ \text{kW}$. Find $v$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Application of $P=Fv$ with $F$ taken as the total resistance” …