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    I've no ideas how to do this question. This is in an M4 mock paper I have, and the answer sheet has no working out. The answer is 56.1m

    A car of mass 1000 kg, moving along a straight horizontal road, is driven by an engine which produces a constant power of 12 kW. The only resistance to the motion of the car is air resistance of magniute 10v² N where v m/s is the speed of the car.

    Find the distance travelled by the car as its speed increases from 5 m/s to 10 m/s

    Power = Fv
    => F = P/v

    Newton's second law:
    F - R = ma
    12000/v - 10v² = 1000 vdv/dx
    1200 - v³ = 100 v² dv/dx
    ∫ dx = -100/3 510 -3v²/(1200 - v³) dv
    x = -100/3 [ln|1200 - v³|]{5, 10} = -100/3 ln|200/1075| = 56.1

    Power = P
    P = Fv
    where F is the driving force from the engine

    P/v - R = mdv/dt

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Updated: June 22, 2005
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