4. A car of mass 900 kg is moving along a straight horizontal road with the engine of the car working at a constant rate of 22.5 kW . At time \(t\) seconds, the speed of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 } ( 0 < v < 30 )\) and the total resistance to the motion of the car has magnitude \(25 v\) newtons.

1. Show that when the speed of the car is \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the acceleration of the car is $$\frac { 900 - v ^ { 2 } } { 36 v } \mathrm {~m} \mathrm {~s} ^ { - 2 }$$ The time taken for the car to accelerate from \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is \(T\) seconds.
2. Show that $$T = 18 \ln \frac { 8 } { 5 }$$
3. Find the distance travelled by the car as it accelerates from \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)