A-level · Work, energy & power

PowerExam-style questions

Power as the rate of doing work, average power = work ÷ time, and the key working relationship P = Fv for a driving force — used to find engine power at constant speed and, by combining P = Fv with Newton's second law, the instantaneous acceleration of a vehicle on a level road or a hill.

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22 questions · A Level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
A car of mass $1500$ kg tows a caravan of mass $1000$ kg down a straight road. The road is inclined to the horizontal at an angle $\alpha$ , where $\sin\alpha = \frac{1}{49}$

The caravan is attached to the car by a tow bar which is parallel to the road. The tow bar is modelled as a light rod.

The non-gravitational resistances to the motion are modelled as constant forces, of magnitude $500$ N on the car and $800$ N on the caravan.

The engine of the car works at a constant rate of $18$ kW.
(a) Find the acceleration of the car and the caravan when their speed is $10\ \text{m s}^{-1}$

(5 marks)

Later, when the car and the caravan are moving down the road at $12\ \text{m s}^{-1}$ , the tow bar breaks. The caravan continues to move down the road and the resistance to its motion is unchanged.
(b) Use the work–energy principle to find how far the caravan travels down the road after the tow bar breaks.

(4 marks)
Level 4 · 9 marksTry it
2
A coach of mass $12\,000$ kg is moving up a straight hill which is inclined to the horizontal at an angle $\alpha$ , where $\sin\alpha = \frac{1}{24}$

The resistance to the motion of the coach from non-gravitational forces is modelled as a constant force of magnitude $R$ newtons. The coach is modelled as a particle.

With its engine working at a constant rate of $72$ kW, the coach moves up the hill at a constant speed of $12\ \text{m s}^{-1}$
(a) Find the value of $R$ .

(4 marks)

While the coach is moving up the hill at $12\ \text{m s}^{-1}$ , the rate at which its engine is working is suddenly increased to $96$ kW.
(b) Find the acceleration of the coach immediately after the rate of working is increased.

(4 marks)

Later, the coach is moving up the hill with speed $15\ \text{m s}^{-1}$ when it passes the point $A$ . At $A$ the engine is switched off. The coach continues to move up the hill and the resistance to its motion is still $R$ newtons.
(c) Use the work–energy principle to find the speed of the coach at the instant when it has travelled $50$ m up the hill from $A$ .

(4 marks)
Level 4 · 12 marksTry it
3
A car of mass $1200\text{ kg}$ travels at a constant speed of $20\text{ m s}^{-1}$ up a hill inclined at angle $\theta$ to the horizontal, where $\sin\theta = 0.05$ . The resistance to motion is constant at $400\text{ N}$ . Taking $g = 10\text{ m s}^{-2}$ , find the power developed by the engine. (5 marks)

(The diagram is not drawn to scale.)
Level 4 · 5 marksTry it
4
A car of mass $800\text{ kg}$ moves along a level road against a constant resistance of $300\text{ N}$ . The engine works at a constant rate of $12000\text{ W}$ . Find the acceleration of the car at the instant when its speed is $15\text{ m s}^{-1}$ . (5 marks)
Level 4 · 5 marksTry it
5
A car of mass $1000\text{ kg}$ moves along a level road with its engine working at $20\text{ kW}$ against a constant resistance of $500\text{ N}$ .

Find the car's acceleration at the instant its speed is $20\text{ m s}^{-1}$ . (4 marks)
Level 4 · 4 marksTry it

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