The average velocity is the total distance moved divided by the total time taken. If you don't know, or cannot compute, the total time taken then there is no way to calculate the average velocity.

There are a number of parameters relevant to the motion:

• time taken, $t$

• initial velocity, $u$

• final velocity, $v$

• acceleration, $a$

• distance moved, $s$

These are related by the SUVAT equations:

$$ v = u + at $$

$$ s = ut + \tfrac{1}{2} at^2 $$

$$ v^2 = u^2 + 2as $$

So given values for some of the parameters we can calculate others. But in your question you specify that all we know is the distance moved, and in this case there is too little information to calculate the values of the other parameters.

Suppose we look at your specific example:

if a car moves with a certain acceleration for a distance $s$ then it moves with a constant velocity for a distance $2s$ and at last it decelerates for a distance $3u$.

In the first stage if we know that the car starts from rest and accelerates with some acceleration $a$ then we can calculate the time taken and final velocity because we know:

$$ s = ut + \tfrac{1}{2} at^2 $$

so given that $u=0$ we get:

$$ t = \sqrt{\frac{2s}{a}} $$

And the average velocity is then distance travelled divided by time taken.

So you can work out what you can calculate by considering what you know and what the SUVAT equations tell you.