In the case of a body freely falling from small height

According to the question we get, 

let us consider the time interval T (t₁ , t₂)

where t₂ - t₁  = c. Where c is the constant 

let us assume that the body is dropped form the rest from a height h.

displacement, S = ut+1/2 at²

S = -$\frac{1}{2}a{t}^2$

position at time t with respective to the ground , x = h -$\frac{1}{2}g{t}^2$

change in position in time interval T,  $∆X= \frac{1}{2}g(t_1^2-t_2^2)$

v = u+at

v = -gt

change in velocity in the time interval will be  Δv = g(t₁​−t₂​) = −gc

as we know that the g is constant an the changes of acceleration is zero in equal intervals of time.