5. A car of mass 1000 kg is towing a trailer of mass 1500 kg along a straight horizontal road. The tow-bar joining the car to the trailer is modelled as a light rod parallel to the road. The total resistance to motion of the car is modelled as having constant magnitude 750 N. The total resistance to motion of the trailer is modelled as of magnitude \(R\) newtons, where \(R\) is a constant. When the engine of the car is working at a rate of 50 kW, the car and the trailer travel at a constant speed of 25 m s\(^{-1}\).
(a) Show that \(R = 1250\). (3)
When travelling at 25 m s\(^{-1}\) the driver of the car disengages the engine and applies the brakes. The brakes provide a constant braking force of magnitude 1500 N to the car. The resisting forces of magnitude 750 N and 1250 N are assumed to remain unchanged. Calculate
(b) the deceleration of the car while braking, (3)
(c) the thrust in the tow-bar while braking, (2)
(d) the work done, in kJ, by the braking force in bringing the car and the trailer to rest. (4)
(e) Suggest how the modelling assumption that the resistances to motion are constant could be refined to be more realistic. (1)
