6. A car of mass 800 kg pulls a trailer of mass 300 kg up a straight road which is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 1 } { 14 }\). The trailer is attached to the car by a light inextensible towbar which is parallel to the direction of motion of the car. The car's engine works at a constant rate of \(P \mathrm {~kW}\). The non-gravitational resistances to motion are constant and of magnitude 600 N on the car and 200 N on the trailer. At a given instant the car is moving at \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is accelerating at \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)

1. Find the value of \(P\). When the car is moving up the road at \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the towbar breaks. The trailer comes to instantaneous rest after moving a distance \(d\) metres up the road from the point where the towbar broke. The non-gravitational resistance to the motion of the trailer remains constant and of magnitude 200 N .
2. Find, using the work-energy principle, the value of \(d\).