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# M2 Power question. watch

1. The resistance to motion of a car moving with speed vm/s is given by the formula (200 + 2v)N. Given that the engine of the car is working at 8kW find the maximum speed of the car as it travels along a horizontal road.

My workings:

P=Fv
8000=Fv
F=8000/v

@ max v, resistive force = driving force

Therefore, 200 + 2v = 8000/v

v(200 + 2v) = 8000
2v^2 + 200v - 8000 = 0
v^2 + 100v - 4000 = 0

and now I'm stuck. Any ideas guys?
2. It's a quadratic - use the formula (can't spot a factorisation straight away, but there probably is one).
3. Done - v=30.6m/s.

Completely forgot about the formula, thanks.

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Updated: September 29, 2011
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