Question

A particle moves from rest, its initial position being given by x = c with reference to a fixed point O. Its acceleration at a distance ‘x’ from 0 is mu/x^2 away from O. Show that its velocity is sqrt mu/c when it is a distance ‘x’ from O.

Answer 1

x'' = mu/x^2 ------>

x'' x' = mu x'/x^2 ----->

1/2 x'^2 = -mu/x + k ------>

x'^2 = -2 mu/x + const.

x'(x = c) = 0 -------->

const. = 2 mu/c --------->

x' = sqrt[2 mu/c - 2 mu/x]