A train accelerates from rest at station $A$ and decelerates to rest at station $B$, a distance $s$ away. Its maximum acceleration is $a_1$ and its maximum deceleration is $a_2$ (in absolute value). A new track-wide speed limit $v_{\max}$ is then imposed. What is the smallest value of $v_{\max}$ for which the minimum travel time between $A$ and $B$ is unchanged?