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

Energy, work and power — practice question

A car of mass $1400\,\text{kg}$ has a resistance-to-motion magnitude of $kv^2\,\text{N}$ when its speed is $v\,\text{m s}^{-1}$, with $k$ as a constant.
(a)

The car travels up a hill at a steady speed of $24\,\text{m s}^{-1}$ on a slope that makes an angle $\alpha$ to the horizontal, where $\sin \alpha = 0.12$. At this speed, the resistance to motion has magnitude $480\,\text{N}$.

(a(i))[1]

Find $k$.

(a(ii))[3]

Calculate the power output of the car’s engine.

(b)[3]

The car now travels at constant speed along a straight level road. If its engine is delivering $54\,\text{kW}$, determine the speed.

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