Question

What is dv/ds? How can it used

Answer 1

dv/ds is a differential form of velocity by displacement. Though this is not directly used for any purpose whatsoever, if you mutliply this with v, it forms v.dv/ds.

v.dv/ds = a ; where a = acceleration and v = velocity.
Explanation: v=dv/dt
v.dv/ds = (dv/dt).(dv/ds) = dv/dt = a