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"A driver of a car suddenly sees the lights of a barrier 40 m ahead; it takes the drive 0.75 s to apply the brakes; the car accelerates at a speed of -10 m/s^2. What is the maximum speed possible?"

I decided to break the problems into two parts; first, the total distance covered during the time prior to initiating of braking and the time after. For the former part I was left with (Vo)(0.75). The latter part I ended with Vo(Vo/10)+0.5(-10)(Vo)^2. I put those together and 40=(Vo)(0.75)+Vo(Vo/10)+0.5(-10)(Vo)^2. Did I create an incorrect equation?