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

Options

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

Answer

C

Explanation

Let velocity of man = u
Distance travelled by man = ut
Distance travelled by bus = `1/2 at^2`
`rArr ut = 45 + 1/2 at^2`
`rArr u = 45/t + 1/2 (2.5) xx t = (45)/(t) + 1.25 t`
To find minimum value of u-
`(du)/(dt) = 0 rArr (-45)/(t^2) + 1.25 = 0 rArr t^2 = 36 rArr t = 6s`
`u_("min) = 45/6 + 1.25 xx 6 = 15m//s`