A particle is falling freely under gravity. In frist `t` secnd it covers distance `d_(1)`and in the next `t` second it covers distance `d_(2)`, then `t` is given by `:`

Options

A. `sqrt((d_(2)+d_(1))/(g)`
B. `sqrt((2(d_(2)+d_(1)))/(g)`
C. `sqrt((d_(2)-d_(1))/(g)`
D. `sqrt((2(d_(2)-d_(1)))/(g)`

Answer

C

Explanation

`d_(1)=(1)/(2)g t^(2)`
and `d_(2)=(g t)t+(1)/(2)g t^(2)rArrd_(2)-d_(1)=g t^(2)`
`rArrt=sqrt((d_(2)-d_(1))/(g)`