A particle is falling freely under gravity. In first t second it covers distance `x_1` and in the next t second, it covers distance `x_2,` then t is given by

Options

A. `sqrt((x_2-x_1)/g)`
B. `sqrt((x_2+x_1)/g)`
C. `sqrt((2(x_2-x_1))/g)
D. `sqrt((2(x_2+x_1))/g)`

Answer

A

Explanation

`x_1=1/2g t^2=0.5 g t^2`
`x_1+x_2=1/2g(2t)^2=2g t^2`
`x_2=2g t^2-x_1=1.5g t^2`
`:. x_2-x_1=g t^2 or t=((x_2-x_1)/g)`