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# M4 kinematics question watch

1. 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
2. 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
3. Power = P
P = Fv
where F is the driving force from the engine

P/v - R = mdv/dt

etc.

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