Question

A man is $45m$ behind the bus when the bus start accelerating from rest with acceleration$2.5m/s^2$. With what minimum velocity should the man start running to catch the bus ?

• A. 12 m/s
• B. 14 m/s
• C. 15 m/s
• D. 16 m/s

Answer 1

The correct option is C 15 m/s

Let man will catch the bus after 't' sec. So, he will cover distance ut.

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

$ut=45+\frac{1}{2}a{t}^2=45+1.25t^2[Asa=2.5m/s^2]$

$\Rightarrow u=\frac{45}{t}+1.25t$

To find the minimum value of u

$\frac{du}{dt}=0$ so we get t = 6 sec then,

$u=\frac{45}{6}+1.25\times 6=7.5+7.5=15m/s.$