Slowing Car Problem Problem: A car is initiall traveling at 200 ft/sec. It begins to coast, but it slowing down due to air resistance, with an acceleration given by a=-(1/1000) v^2. Compute the velocity and position functions. Will the car travel a finite or an infinite distance? Let v(t) denote the velocity at time t. We have the following diifferential equation for v(y). 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JSFH JSFH We can also solve for v as a function of x directly as follows. By the chain rule, dv/dt=dv/dx* dx/dt= dv/dx*v. 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