What are the variables in the formula for average acceleration?

[MienTommy]

The formula for average acceleration is (v_final - v_initial) / (t_initial - t_final), I was wondering if v_initial and _final are the instantaneous velocities (found by second derivative of a function) at those points or are they the average velocities (found by change in distance over time)? It has been a while since I've done physics.

 

[mathman]

Instantaneous velocities.

 

[MuIotaTau]

They are instantaneous velocities, yes.