CAIE A-Level Mathematics 4.5 Energy, Work and Power Question Bank

A crate is being pushed in a straight line along a horizontal surface by a force of magnitude 25 N inclined at $20^{\circ}$ above the horizontal. The crate moves a distance of 12 m in 8 seconds with constant speed.

A car of mass 900 kg is moving along a straight horizontal road against a constant resistance to motion of 350 N . At an instant when the car is moving at $15 \mathrm{~ms}^{-1}$ its acceleration is $0.25 \mathrm{~ms}^{-2}$.

Find the power of the car's engine at this instant.

A car of mass 800 kg is moving on a straight road.
When the car is moving at a constant speed of $20 \mathrm{~ms}^{-1}$ on a horizontal section of the road, the engine of the car is working at $P \mathrm{~W}$.

When the car is moving at a constant speed of $12 \mathrm{~ms}^{-1}$ up a section of the road inclined at $\sin ^{-1} 0.15$ to the horizontal, the engine of the car is also working at $P \mathrm{~W}$.

On both sections of the road there is a constant force of magnitude $R \mathrm{~N}$ resisting the motion of the car.

Two particles, A and B, of masses $m \mathrm{~kg}$ and 3 kg respectively, are connected by a light inextensible string. Particle B is on a fixed plane which is at an angle of $\sin ^{-1} 0.6$ to the horizontal ground. The string passes over a fixed smooth pulley at the top of the plane. Particle A hangs vertically below the pulley and is 0.75 m above the ground (see diagram).

The system is released from rest. In the subsequent motion B moves up a line of greatest slope of the plane and does not reach the pulley. As B moves up the plane there is a constant resistance to its motion of magnitude $\frac{10}{3} \mathrm{~N}$. The speed of A immediately before it hits the ground is $2 \mathrm{~ms}^{-1}$.

Use an energy method to find the value of m.

A car of mass 1600 kg travels at constant speed $20 \mathrm{~m} \mathrm{~s}^{-1}$ up a straight road inclined at an angle of $\sin ^{-1} 0.12$ to the horizontal.