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Driver A has boon leading archrival B for a while by a steady 3 miles. Only 2 miles from the finish, driver A ran out of gas and decelerated thereafter at ta rate proportional to the square of his remaining speed. One mile later,driver A's speed was exactly halved.If driver B's speed remained constant,who won the race?

i have tried the set up the relation$d^2x\over dt^2$=$K ({dx\over dt})^2$ and integrate it but dont know how to do.

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Can you update your post and let us know what you've already tried, or which part of the question you don't understand? Also, if this is homework, then you should add the homework tag. –  Chris Taylor Feb 2 '12 at 8:03
Also it isn't homework question in fact.Just a question in a textbook –  Mathematics Feb 2 '12 at 8:12
Hint: Try writing $v=dx/dt$ so that your equation becomes $dv/dt = -kv^2$ and try to separate variables. –  Chris Taylor Feb 2 '12 at 8:45
Hint : $$\frac{\ddot x}{\dot x}=\frac{d \dot x}{dx}$$ –  pedja Feb 2 '12 at 10:04

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