A-LevelMathematicsMechanics9709/42 · Feb/Mar 2020 · Q69 Marks

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 ms⁻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 ms⁻¹ and the car and trailer continue moving in the same direction with speed 2 ms⁻¹. Find the mass of the van.[3]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

[M1] Apply Newton's 2nd law to the trailer or apply Newton's 2nd law to the car and to the system and eliminate the braking force, F.
[A1]
[M1] Apply Newton's second law either to the car or to the system with braking force = F and use of their T from 6(a)
[A1]
[M1] A complete method using constant acceleration equations which would lead to an equation for finding v, using u = 22, s = 17.5 and a = –12
[A1] AG
[M1] For applying the conservation of momentum equation to the system of car, trailer and van, where m = mass of the van
[A1] Correct equation
[A1]

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