1. A car of mass 1000 kg moves along a straight horizontal road.

In all circumstances, when the speed of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the resistance to the motion of the car is modelled as a force of magnitude \(c v ^ { 2 } \mathrm {~N}\), where \(c\) is a constant. The maximum power that can be developed by the engine of the car is 50 kW .
At the instant when the speed of the car is \(72 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) and the engine is working at its maximum power, the acceleration of the car is \(2.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)

1. Convert \(72 \mathrm {~km} \mathrm {~h} ^ { - 1 }\) into \(\mathrm { m } \mathrm { s } ^ { - 1 }\)
2. Find the acceleration of the car at the instant when the speed of the car is \(144 \mathrm { kmh } ^ { - 1 }\) and the engine is working at its maximum power. The maximum speed of the car when the engine is working at its maximum power is \(V \mathrm {~km} \mathrm {~h} ^ { - 1 }\).
3. Find, to the nearest whole number, the value of \(V\).