That is not entirely correct. Consider this:
Acceleration/Formula
= average acceleration
=
final velocity
= starting velocity
= elapsed time
From the web
Acceleration (a) is the change in
velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt. This allows you to measure how fast
velocity changes in meters per second squared (m/s^2). Acceleration is also a vector quantity, so it includes both magnitude and direction.
So, δV is always going to be faster than v-sub, that is just physics.
But if a mass is always accelerating (which is not possible) the velocity is null, at any point on a line. This is the reason for the v-sub variable. Yea, it confuses me too but it is a constant.
The easier way for me to think about it is to say an object can neither instantly start moving at a velocity nor can it instantly stop. This is part of being the vector quantity mentioned.
In motion control we often have to calculate final velocity from a 'flying' start. When considering the final destination (if relevant) the vector quantity usually has a higher value than δt since mass is complex and time is constant.
I think what you are saying is defined as ramp. The angle of acceleration. If you look at them on a plane you can much easier understand the difference between v and v-sub.
Hope this makes sense.
***Note: I can never get certain ASCII characters to work on this site.