That is if by "delta velocity" you mean the difference between two velocities.
Say you have Vo and V1.
delta V = V1 -Vo
average V = (Vo +V1)/2
They can never be the same.
The average velocity in the interval [t1, t2] is defined as:
I can easily think of an example where delta v and <v> are the same...
Let's consider motion in interval [0, 2s] on the straight line, with constant accelelation . Let's assume that initial velocity is equal . One can easily check that:
We can get a simple relation between distanse and average velocity:
If you like arithmetic mean you should observe that "average velocity" is equal to arithmetic mean if accelelation is constant.
where the x's are displacements.
I also agree that Ticbol's average velocity is not at all general, as it presupposes a constant acceleration in order to have that form.
Frankly speaking it is the matter of terminology....
Unfortunatelly I'm not very familiar with physics, english terminology...it can cause some problems...
In polish terminology there is the distinction between "velocity" (prędkość) and "speed" (szybkość)...
As "speed" I consider modulus of "velocity" - scalar quantity. "Velocity" is of a course vector...
The average "speed" is defined with the above integral...
What's with the average "velocity", it is analogous, so it is defined with the integral:
Obviously this definition is equivalent to yours because: