7 A car of mass 1200 kg moves in a straight line along horizontal ground. The resistance to motion of the car is constant and has magnitude 960 N . The car's engine works at a rate of 17280 W .
- Calculate the acceleration of the car at an instant when its speed is \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
The car passes through the points \(A\) and \(B\). While the car is moving between \(A\) and \(B\) it has constant speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
- Show that \(V = 18\).
At the instant that the car reaches \(B\) the engine is switched off and subsequently provides no energy. The car continues along the straight line until it comes to rest at the point \(C\). The time taken for the car to travel from \(A\) to \(C\) is 52.5 s .
- Find the distance \(A C\).