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

Energy, work and power — practice question

A car with mass $1200\,\text{kg}$ can move at a maximum constant speed of $60\,\text{m s}^{-1}$ on a straight horizontal road. When the car is moving at $v\,\text{m s}^{-1}$, the resistive force has magnitude $35v\,\text{N}$.
(i)[2]

Find the car’s greatest possible power.

(ii)[3]

The car moves on a straight horizontal road. Show that, at the instant when its speed is $30\,\text{m s}^{-1}$, the car’s greatest possible acceleration is $2.625\,\text{m s}^{-2}$.

(iii)[5]

The car moves up a hill at constant speed, where the hill is inclined at an angle of $\sin^{-1}\!\left(\frac{7}{48}\right)$ to the horizontal. Find the car’s greatest possible speed.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Driving force found from $35 \times 60$

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