At time t = 0, two bodies A and B at the same point. A moves with constant velocity `upsilon` and B starts from rest and moves with constant acceleration. Relative velocity of B w.r.t. A when the bodies meet each other is

Options

A. `(upsilon)/(2)`
B. `(upsilon)/(3)`
C. `upsilon`
D. `2upsilon`

Answer

C

Explanation

`A rarr upsilon_(A)` (constant velocity)
`B rarr a` (constant acceleration)
C be the fixed point at which both A and B meet in time t
Now, `s=updilon_(A)t` and `upsilon_(B)=at`
`A rarr upsilon_(A)=upsilon`

`s=(1)/(2)at^(2)=upsilon_(A)t`
`a=(2upsilon_(A))/(t)rArr upsilon_(B)=at=2upsilon_(A)`
`upsilon_(BA)=` velocity of B w.r.t. A
`rArr upsilon_(BA)=upsilon_(B)-upsilon_(A)=2upsilon_(A)-upsilon_(A)=upsilon_(A)`
`rArr upsilon_(BA)=upsilon " " (therefore upsilon_(A)=upsilon)`