On a straight horizontal test track, driverless vehicles (with no passengers) are being tested. A car of mass 1600 kg is towing a trailer of mass 700 kg along the track. The brakes are applied, resulting in a deceleration of 12 m s^-2. The braking force acts on the car only. In addition to the braking force there are constant resistance forces of 600 N on the car and of 200 N on the trailer.

(a) Find the magnitude of the force in the tow-bar. [2]

(b) Find the braking force. [2]

(c) At the instant when the brakes are applied, the car has speed 22 m s^-1. At this instant the car is 17.5 m away from a stationary van, which is directly in front of the car. Show that the car hits the van at a speed of 8 m s^-1. [2]

(d) After the collision, the van starts to move with speed 5 m s^-1 and the car and trailer continue moving in the same direction with speed 2 m s^-1. Find the mass of the van. [3]