A car of mass \(2000\text{ kg}\) travels in a straight line on a horizontal road. The car accelerates from \(10\text{ m s}^{-1}\) to \(20\text{ m s}^{-1}\) in \(8\text{ s}\). Assume that resistance can be ignored.

Use the work-energy principle to find the work done by the driving force.

Enter just the number in joules.

A car of mass \(2000\text{ kg}\) accelerates from \(10\text{ m s}^{-1}\) to \(20\text{ m s}^{-1}\) in \(8\text{ s}\) on a horizontal road. Resistance can be ignored.

Find the average power generated by the engine.

Enter just the number in kW.

The engine of a \(5\text{ tonne}\) truck has a power output of \(400\text{ kW}\). The truck is travelling in a straight line on a horizontal road. The resistance to motion is \(20000\text{ N}\).

Find the maximum speed the truck could achieve.

Enter just the number.

The maximum power of a boat engine is \(140\text{ kW}\). The boat is subject to a resistance force of \(10000\text{ N}\).

Find the maximum speed the boat can achieve when travelling in a straight line.

Enter just the number.

A model train of mass \(200\text{ g}\) is moving in a straight line on a level track. The train accelerates from \(2\text{ m s}^{-1}\) to \(8\text{ m s}^{-1}\) in \(3\text{ s}\).

Find the average power generated by the engine.

Enter just the number in watts.

The maximum power of a boat engine is \(120\text{ kW}\). The maximum speed the boat can achieve is \(10\text{ m s}^{-1}\).

Find the resistance force acting on the boat when it is travelling at its maximum speed and the engine is working at maximum power.

Enter just the number in newtons.

A car of mass \(1800\text{ kg}\) is being driven, at a constant \(15\text{ m s}^{-1}\), against a resistance of \(2000\text{ N}\), up a hill inclined at \(10^\circ\) to the horizontal.

Find the rate at which the engine is working.

Enter just the number in kW.

A car of mass \(1600\text{ kg}\) is being driven up a hill inclined at \(10^\circ\) to the horizontal. The car has an initial speed of \(10\text{ m s}^{-1}\) and a final speed of \(12\text{ m s}^{-1}\) after \(60\text{ s}\). Air resistance and friction may be ignored.

Find the average power generated by the engine.

Enter just the number in kW.

A car of mass \(1200\text{ kg}\) accelerates up a hill against a resistance of \(263\text{ N}\). At a certain point on the hill the road is inclined at \(8^\circ\) to the horizontal. The engine is working at \(75\text{ kW}\) and the car is travelling at \(25\text{ m s}^{-1}\).

Find the acceleration of the car at this instant.

Enter just the number.

A small van of mass \(1600\text{ kg}\) accelerates from rest in a straight line along a horizontal road. The resistance from friction and air resistance is \(2400\text{ N}\) throughout the motion. The engine works at a constant rate of \(48\text{ kW}\).

Which expression gives the driving force when the van is travelling at \(v\text{ m s}^{-1}\)?

A small van of mass \(1600\text{ kg}\) moves on a horizontal road. The engine power is constant at \(48\text{ kW}\), and the total resistance is \(2400\text{ N}\).

Which expression gives the acceleration when the van is travelling at \(v\text{ m s}^{-1}\)?

A van is modelled as moving with constant engine power from rest.

Why cannot this power model hold at the instant when the van starts from rest?