A car of mass 1500 kg is pulling a trailer of mass 300 kg along a straight horizontal road at a constant speed of 20 m s⁻¹. The system of the car and trailer is modelled as two particles, connected by a light rigid horizontal rod. The power of the car's engine is 6000 W. There are constant resistances to motion of RN on the car and 80 N on the trailer.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.

1. [B1] Using F = P/v Driving force = 6000/20 [= 300 N]
2. [B1ft] Net force on system = 300 – R – 220 = 0 ft on DF found R = 300 – 80 = 220
3. [M1] Any one equation from the following: Apply Newton's 2nd law to the car / Apply Newton's 2nd law to the trailer / Apply Newton's 2nd law to the system of car and trailer. [New driving force DF = 12500/25 = 500 N]
4. [A1ft] Correct DF = 500 must be used. ft on R value found
5. [M1] EITHER solve two dimensionally correct simultaneous equations in a and T to find a or T OR solve the system equation to find a [Car: DF-T-R = 1500a, Trailer: T-80 = 300a, System: DF – 80 – R = 1800a]
6. [A1] Allow a = 1/9 a = 0.111 m s⁻²
7. [A1] Allow T = 340/3 T = 113 N (= 113.3333...)