A particle executes `SHM` on a straight line. At two positions, its velocities are `u` and `v` whle accelerations are `alpha` and `beta` respectively `[beta gt alpha gt ]`.The distance between these two positions is

Options

A. `(u^(2)+v^(2))/(alpha+beta)`
B. `(u^(2)-v^(2))/(alpha+beta)`
C. `(u^(2)-v^(2))/(beta-alpha)`
D. `(u^(2)+v^(2))/(beta-alpha)`

Answer

B

Explanation

`V = omega sqrt(A^(2) -x^(2)) , a =omega^(2)x`