A bus starting from rest moves with a uniform acceleration of $0.1\ ms^{-2}$ for 2 minutes. Find $ (a) $ the speed acquired, (b) the distance travelled.

$( a)$. Here, Initial velocity $u=0$

Acceleration $a=0.1\ ms^{-2}$

Time $t=2\ minutes=2\times60=120\ second$

On using the equation of motion $v=u+at$

Speed acquired $v=0+0.1\times120$

$=0+12$

$=12\ m/s$

$( b)$.  On using the equation of motion $v^2=u^2+2as$

$12^2=0+2\times0.1\times s$

Or $144=0+0.2s$

Or $s=\frac{144}{0.2}$

Or $s=720\ m$

Thus, the distance travelled is $720\ m$.