A-LevelMathematicsMechanics9709/43 · Oct/Nov 2020 · Q610 Marks
A car of mass 1600 kg is pulling a caravan of mass 800 kg. The car and the caravan are connected by a light rigid tow-bar. The resistances to the motion of the car and caravan are 400 N and 250 N respectively.
- (a)(i)Given that the car and caravan have a constant speed of 25 m s¯¹, find the power of the car's engine.[2]
- (a)(ii)The engine's power is now suddenly increased to 39 kW. 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 of sin¯¹ 0.05 to the horizontal, at a constant speed of v m s¯¹. The car's engine is working at 32.5 kW. Find v.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [1] Use P = Fv with F = total resistance
- [1] Accept 16 300 W or 16.3 kW (3sf)
- [1] For using DF = P/v
- [1] [1560-650 = 2400 × a]
- [1] Two correct equations
- [1] For solving for a or for T
- [1] a = 0.379 ms-2 (0.37916...) T = 553 N (553.33...)
- [1] Newton's 2nd law
- [1] For using P = Fv
- [1] v = 17.6 (Allow v = 650/37)
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