Two particles start moving from the same point along the same straight line. The first moves with constant velocity `v` and the second with constant acceleration `a`. During the time that elapses before the sound catches the first, the greatest distance between the particle is.

Options

A. `(v^2)/(a)`
B. `(v^2)/(2 a)`
C. `(2 v^2)/(a)`
D. `(v^2)/(4 a)`

Answer

B

Explanation

Let `x` be the distance between the particles after `t` seconds. Then
`x = vt - (1)/(2) at^2` …(1)
For `x` to be maximum
`(dx)/(dt) = 0`
or `v - at = 0`
or `t = (v)/(a)`
substituting this value in (1) we get
`x = v((v)/(a)) - (1)/(2) a((v)/(a))^2`
or `x = (v^2)/(2a)`.