May/June 2026 Paper 41

A car of mass $1200\mathrm{kg}$ is moving on a straight horizontal road. The resistance to the motion of the car has a constant magnitude of $600\mathrm{N}$ and the car's engine is working at a rate of $27\mathrm{kW}$. Find the acceleration of the car when its speed is $18m/s$.

The car now moves up a straight hill which is inclined at an angle $\theta$ to the horizontal. The resistance to the motion of the car has now changed to a constant magnitude of $650\mathrm{N}$. The car moves up the hill at a constant speed of $12m/s$ with the car's engine working at a rate of $22\mathrm{kW}$. Find the value of $\theta$.