A particle executes SHM on a straight line. At two positions, its velocities are u and v while accelerations are α and ß respectively [ß > α > 0] . The distance between these two positions is

A particle executes SHM on a straight line. At two positions, its velocities are u and v while accelerations are α and ß respectively [ß > α > 0] . The distance between these two positions is

A
$\frac{u^{2} + v^{2}}{α + β}$
B
$\frac{u^{2} - v^{2}}{α + β}$
C
$\frac{u^{2} - v^{2}}{β - α}$
D
$\frac{u^{2} + v^{2}}{β - α}$

Solution:

$V = ω \sqrt{A^{2} - x^{2}}; a = ω^{2} x$

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