4. 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 m s–1, the resistance to the motion of the car is modelled as a force of magnitude (200 + ) N, where 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 m s–1 (a) Show that = 8 (4) Later on, the car is pulling the trailer up a straight road inclined at an angle to the horizontal, where sin = The resistance to the motion of the trailer from non-gravitational forces is modelled as a constant force of magnitude 200 N at all times. At the instant when the speed of the car is v m s–1, the resistance to the motion of the car from non-gravitational forces is modelled as a force of magnitude (200 + 8v) N. The engine of the car is again working at a constant rate of 15 kW. When v = 10, 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. (b) Find the acceleration of the car immediately after the towbar breaks. (4) (c) Use the work-energy principle to find the value of d. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________