5 A car of mass 850 kg is travelling along a straight horizontal road. The power developed by the car is constant and is equal to 18 kW . There is a constant resistance to motion of magnitude 600 N .
- Find the greatest steady speed at which the car can travel.
Later in the journey, while travelling at a speed of \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the car comes to the bottom of a straight hill which is inclined at an angle of \(\sin ^ { - 1 } \left( \frac { 1 } { 40 } \right)\) to the horizontal.
The power developed by the car remains constant at 18 kW . The magnitude of the resistance force is no longer constant but changes such that the total work done against the resistance force in ascending the hill is 103000 J . The car takes 10 seconds to ascend the hill and at the top of the hill the car is travelling at \(18 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Determine the distance the car travels from the bottom to the top of the hill.