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

Options

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

Answer

C

Explanation

For particle `1` moving with constant velocity ,
` S_1 = 50 t`.
For particle `2` moving with constant acceleration,
` S_2 = 1/2 at^2 = 1/2 xx 10t^2 = 5t^2 , As per question , ltbRgt ` S-2 - S_1 = 12 5` or ` 5 t^2 - 50 t= 125`
or ` t^2 - 10 t- 25 =0`
On solving we ger,` t= (5 +-5 sqrt 2 ) sec.
` t=(5+5 sqrt 2) sec`.