The velocity (v) of a particle (under a force F ) depends on its distance (x) from the origin (with x>0) v 1 x . Find how the magnitude of the force (F) on the particle depends on x ?

Step-by-step solution

According to the question. v 1 x or v= k x d v d t = d d t K x =k -1 2 x^ - 1 2 -1 d x d t a=- k 2 x^ - 3 2 k x [ d x d t =v . and v= k x from . Eq (i) ] = -k² 2 1 x² =m k² 2 1 x² (magnitue F= k² 2 m x² x 1 x²