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

Answer

B

Explanation

Method I:
For greatest distance, `v_1 = v_2`
so, `v = (0 + at) implies t = v/a` and separation `= DeltaS `
`= vt – (0 + 1/2at^2) = vt – 1/2 at^2`
`= v (v/a) - 1/2 a (v/a)^2 = (v^2)/(2a)`
Method II:
For greatest distance `v_("rel") = 0`
so, `0^2 = u_("rel")^(2) + 2a_("rel" S_("rel")`
`to S_("rel") - ((v - 0)^2)/(2(a - 0)) - (v^2)/(2a)`