A man is d distance behind the bus when the bus starts accelerating from rest with an acceleration `a_(0)`. With what minimum constant velocity should the man start running to catch the bus

Options

A. `sqrt(4a_(0)d)`
B. `sqrt(3a_(0)d)`
C. `sqrt(2a_(0)d)`
D. `sqrt(a_(0)d)`

Answer

C

Explanation

The man catches the bus at point `P`, after time t (uniform motion):
`d+s=v t …(i)`
(accelerated motion):
`s=0+1/2a_(0)t^(2) …(ii)`
From (i) and (ii)
`d+1/2a_(0)t^(2)=vt`
`a_(0)t^(2)-2v t+2d=0`
The man will catch the bus, if time t is real, for time t to be real
`[(-2v)^(2)-4 a_(0).2d]ge0`
`v^(2)-2 a_(0)dge0`
`vgesqrt(2a_(0)d)`
`v_("min")=sqrt(2a_(0)d)`