5 A car is towing a trailer along a straight road using a light tow-bar which is parallel to the road. The masses of the car and the trailer are 900 kg and 250 kg respectively. The resistance to motion of the car is 600 N and the resistance to motion of the trailer is 150 N .

1. At one stage of the motion, the road is horizontal and the pulling force exerted on the trailer is zero.
   (a) Show that the acceleration of the trailer is \(- 0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
   (b) Find the driving force exerted by the car.
   (c) Calculate the distance required to reduce the speed of the car and trailer from \(18 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) to \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
2. At another stage of the motion, the car and trailer are moving down a slope inclined at \(3 ^ { \circ }\) to the horizontal. The resistances to motion of the car and trailer are unchanged. The driving force exerted by the car is 980 N . Find
   (a) the acceleration of the car and trailer,
   (b) the pulling force exerted on the trailer.