Explanation

In one dimensional motion, for the maximum and minimum displacement we must have the magnitude and direction of maximum velocity. As maximum velocity in positive direction is $v_{0}$, hence maximum velocity in opposite direction is also $-v_{0}$. Maximum displacement in one direction = $v_{0}T$ Maximum displacement in opposite directions = $-v_{0}T$. Hence, $-v_{0}T < x < v_{0}T$