A truck of mass 1800 kg is towing a trailer of mass 800 kg up a straight road which is inclined to the horizontal at an angle \(\alpha\), where \(\sin \alpha = \frac { 1 } { 20 }\). The truck is connected to the trailer by a light inextensible rope which is parallel to the direction of motion of the truck. The resistances to motion of the truck and the trailer from non-gravitational forces are modelled as constant forces of magnitudes 300 N and 200 N respectively. The truck is moving at constant speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the engine of the truck is working at a rate of 40 kW .
Find the value of \(v\).
As the truck is moving up the road the rope breaks.
Find the acceleration of the truck immediately after the rope breaks.