7 A car of mass 1200 kg is travelling along a straight horizontal road. The power of the car's engine is constant and is equal to 16 kW . There is a constant resistance to motion of magnitude 500 N .

1. Find the acceleration of the car at an instant when its speed is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. Assuming that the power and the resistance forces remain unchanged, find the steady speed at which the car can travel.
   The car comes to the bottom of a straight hill of length 316 m , inclined at an angle to the horizontal of \(\sin ^ { - 1 } \left( \frac { 1 } { 60 } \right)\). The power remains constant at 16 kW , but the magnitude of the resistance force is no longer constant and changes such that the work done against the resistance force in ascending the hill is 128400 J . The time taken to ascend the hill is 15 s .
3. Given that the car is travelling at a speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the bottom of the hill, find its speed at the top of the hill.
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