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.

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.

Count Iblis · Answer

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]