1. A car of mass 600 kg pulls a trailer of mass 150 kg along a straight horizontal road. The trailer is connected to the car by a light inextensible towbar, which is parallel to the direction of motion of the car. The resistance to the motion of the trailer is modelled as a constant force of magnitude 200 N. At the instant when the speed of the car is v ms^–1, the resistance to the motion of the car is modelled as a force of magnitude $(200+ \lambda v)N$, where $\lambda$ is a constant.

When the engine of the car is working at a constant rate of 15 kW, the car is moving at a constant speed of 25 ms^–1.

Show that $\lambda =8$.