Mathematics 9709 · AS & A Level · Energy, work and power

Energy, work and power — practice question

A car with mass $800\text{ kg}$ travels along a straight road. It runs at constant speed $20\text{ m s}^{-1}$ on a horizontal stretch, and in that situation the engine delivers $P\text{ W}$. It also runs at constant speed $12\text{ m s}^{-1}$ on a stretch that slopes upward at $\sin^{-1}0.15$ to the horizontal, and there too the engine delivers $P\text{ W}$. On each stretch, a constant force of magnitude $R\text{ N}$ opposes the car’s motion.
(a)[5]

Find the values of $R$ and $P$.

(b)[3]

Find the acceleration of the car as it travels at $10\,\text{m s}^{-1}$ up the sloping section of road while the engine works at $32\,\text{kW}$.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Driving force recognised as $\frac{P}{12}$ or $\frac{P}{20}$

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