Explain how the average velocity of free electrons ...

It is true the electrons are accelerated when put in an electrical field but they have something that is stopping them from leaving the metal and that thing is the air.

Let us think of an electrical current. The electrons move through a metal wire to produce a current but if the wire ends the electrons won't continue to travel through the air because of its properties. the same thing happens if you put a piece of metal in an electrical field. the electrons will rearrange in such a way that will create more negative charge on one side of the metal and more positive charge on the other, but the electrons won't take off in to the air and fly away from the metal. Hope this explanation was clear.

Please observe Ohm's Law: E=I/R. 

Where E=electromotive force (rated in volts)

I=Inductive force (rated in amperes)

R=Resistance (rated in ohms).

We see an inverse ratio of electrical current proportional to the voltage applied.  The higher the voltage, the more current the line will draw, if resistance remains constant.

Alternatively:  P=I^2 R.

Where P=power working through a line

I=current (in amperes)

R= resistance (in ohms).

More precisely: AC is a scalar field that interacts on the outside of a line, using the conductor to transmit electromotive force.