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

Energy, work and power — practice question

$AB$ and $BC$ are straight roads with inclinations of $5^\circ$ to the horizontal and $1^\circ$ to the horizontal respectively. $A$ and $C$ lie at the same horizontal height, while $B$ is $45\,\text{m}$ above the level of $A$ and $C$. A car with mass $1200\,\text{kg}$ moves from $A$ to $C$ via $B$.
(i)[3]

For the journey from $A$ to $B$, the car moves with constant speed and the work done against the resistance to motion is $360\,\text{kJ}$. Find the work done by the car’s engine from $A$ to $B$.

(ii)[4]

For the motion from $B$ to $C$ the work done by the driving force is $1660\,\text{kJ}$. Given that the speed of the car at $B$ is $15\,\text{m s}^{-1}$, show that its speed at $C$ is $29.9\,\text{m s}^{-1}$, correct to $3$ significant figures.

(iii)[3]

Immediately after leaving $B$, the car’s driving force is $1.5$ times the driving force immediately before reaching $C$. Find, correct to $2$ significant figures, the ratio of the power developed by the car’s engine immediately after leaving $B$ to the power developed immediately before reaching $C$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate increase in PE $= 1200g \times 45$” …

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