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A man is 45 m behind the bus when the bu...

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?

A

12m/s

B

14m/s

C

15m/s

D

16m/s

Text Solution

Verified by Experts

The correct Answer is:
C
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`
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