Similarly distance travelled by the bus will be $\frac{1}{2}a{t^2}$ for the given condition

$ut = 50 + \frac{1}{2}a{t^2} = 50 + \frac{{{t^2}}}{2}$  [$a = 1\;m/{s^2}$]

$⇒$ $ u  = \frac{{50}}{t} + \frac{t}{2}$

To find the minimum value of $u$

$\frac{{du}}{{dt}} = 0$, so we get $t = 10\sec $, then $u = 10\;m/s$