Two particles, one with constant velocity `50 m//s` and the other with uniform acceleration `10m//s^(2)`, start moving simultaneously from the same position in the same direction. They will be at a distance of `125m` from each other after

Options

A. `5` sec
B. `5(1 + sqrt(2))` sec
C. `10` sec.
D. `10(sqrt(2) + 1)` sec

Answer

A, B

Explanation

Displacement of particle `1` after time `t`,
`x_(1) = 50t`
Displacement of particle `2` after time `t`,
`x_(2) = (1)/(2) xx 10 xx t^(2) = 5t^(2)`
According to question,
`5t^(2) - 50t = 125` or `50t - 50t^(2) = 125`
`rArr t^(2) - 10t - 25 = 0` or `t^(2) - 10t + 25 = 0`
`rArr t = 5(1 + sqrt(2))` or `t^(2) = 5 sec`.