Suppose that the velocity of a falling body is v = k/s (k a constant) at the instant the body has fallen s meters from its starting point. Find the body's acceleration as a function of s.

Answer 1

v = Vi + a t = 0 + a t
= a t = k/s
so
t = k/(a s)

s = 0 + . 5 a t^2
= .5 a t^2

s = .5 a k^2/(a^2 s^2)
s^3 a = .5 k^2
a = .5 k^2/s^3