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

Energy, work and power — practice question

A car with mass $1250\,\text{kg}$ travels from the foot to the summit of a straight hill that is $500\,\text{m}$ long. The top is $30\,\text{m}$ above the level of the bottom. The car’s engine has a constant power of $30\,000\,\text{W}$. At the bottom of the hill, the car’s acceleration is $4\,\text{m s}^{-2}$, and at the top it is $0.2\,\text{m s}^{-2}$. The resistance opposing the car’s motion is $1000\,\text{N}$.
(i)[5]

Find the increase in the car’s kinetic energy.

(ii)[3]

Find the work done by the engine of the car.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Driving force relation $DF = \frac{30000}{v}$

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