Problems from SolvingPhysics #2

A train is moving rectilinearly with a velocity $\displaystyle \upsilon =180{ km }/{ hr }$ . Suddenly an obstacle appears on the tracks and the brakes are applied.Now the velocity of the rain changes according to $\displaystyle \nu =\upsilon -\alpha { t }^{ 2 }$ with $\displaystyle \alpha =1{ m }/{ { s }^{ 2 } }$ . What is the breaking distance (x) of the train?How much time (t) must pass from the moment the brakes are applied before the train stops?

If absolute value of the breaking distance is 'x' and absolute value of the time passed 't' . Find x+t .

[Use S.I units]