A-LevelMathematicsMechanics9709/43 · Oct/Nov 2022 · Q610 Marks

A car of mass 1750kg is pulling a caravan of mass 500kg. The car and the caravan are connected by a light rigid tow-bar. The resistances to the motion of the car and caravan are 650N and 150N respectively.

(a)(i)Find the power of the car's engine.[2]
(a)(ii)The engine's power is now suddenly increased to 40kW. Find the instantaneous acceleration of the car and caravan and find the tension in the tow-bar.[5]
(b)The car and caravan now travel up a straight hill, inclined at an angle sin¯¹ 0.14 to the horizontal, at a constant speed of vms¯¹. The car's engine is working at 31 kW. The resistances to the motion of the car and caravan are unchanged. Find v.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

[M1] P = (650+150) × 24 Use of P = DF × v.
[A1] 19200 W or 19.2kW
[B1] 40 000 = DF × 24 Correct use of P = DF × v.
[M1] 40000/24 - 800 = 2250a Use of Newton's Second Law for the system or for the caravan or for the car.
[A1] T-150=500a Two correct equations.
[M1] a=(40000/24 - 800)/2250 leading to a = ... Solves for a or for T.
[A1] Acceleration = 0.385 ms-2 and Tension = 343 N From a = 52/135 = 0.38518.... and T = 9250/27 = 342.59...
[M1] DF = 800+2250×g×0.14 Resolving up hill using DF = Total resistances.
[M1] 31000/v =800+2250×g×0.14 Use of P = DF × v to form equation in v.
[A1] v = 7.85 From v = 620/79 = 7.848...

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