2 A car of mass 1500 kg travels along a straight horizontal road. The resistance to the motion of the car is \(k v ^ { \frac { 1 } { 2 } } \mathrm {~N}\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the speed of the car and \(k\) is a constant. At the instant when the engine produces a power of 15000 W , the car has speed \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is accelerating at \(0.4 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Find the value of \(k\). It is given that the greatest steady speed of the car on this road is \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. Find the greatest power that the engine can produce.