6 A car of mass 1250 kg moves from the bottom to the top of a straight hill of length 500 m . The top of the hill is 30 m above the level of the bottom. The power of the car's engine is constant and equal to 30000 W . The car's acceleration is \(4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) at the bottom of the hill and is \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\) at the top. The resistance to the car's motion is 1000 N . Find

1. the car's gain in kinetic energy,
2. the work done by the car's engine.