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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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    **Hint:** Try writing $v=dx/dt$ so that your equation becomes $dv/dt = -kv^2$ and try to separate variables.2012-02-02
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    Hint : $$\frac{\ddot x}{\dot x}=\frac{d \dot x}{dx}$$2012-02-02

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