Two objects move in the same direction in a straight line. One moves with a constant velocity `v_(1)`. The other starts at rest and has constant acceleration a. They collide when the second object has velocity `2v_(1)`. The distance between the two objects when the second one starts moving is :-

Options

A. zero
B. `(v_(1)^(2))/(2a)`
C. `(v_(1)^(2))/(a)`
D. `(2v_(1)^(2))/(a)`

Answer

A

Explanation

For second object
`2v_(1) = 0 +` at, `t = (2v_(1))/(a)` ….(i)
`s_(1) = s_(2) + d, (1)/(2)at^(2) = ut + d`
`rArr (1)/(2)a xx ((2v_(1))/(a))^(2) = v_(1)((2v_(1))/(a)) + d rArr d = (2v_(1)^(2))/(a) - (2v_(1)^(2))/(a) = 0`