kinetic friction

You're right. In practice, the coefficient of friction may depend on the relative surface speed as well as contact area.

The coefficient of kinetic friction is approximately constant only for certain types of surfaces and low surface pressure (i.e. normal reaction per unit area). This type of friction is known as Coulomb friction. The original of Coulomb friction is not due to the roughness of two sliding surfaces but the electromagnetic interaction between the atoms on the two surfaces. It is assumed that the surfaces are in atomically close contact only over a small fraction of their overall area. And this area is in proportion to the normal force (surface pressure x total contact area). So, Coulomb friction depends only on the normal force but is independent of the contact area and relative surface speed. At high surface pressure, the assumption for Coulomb friction may no longer hold and the coefficient of friction is not constant any more.

In practice, the coefficient of friction may depend on a lot of factors. It can be very complicated and not all can be explained in terms of mathematical theory. The coefficients are maily determined experimetally. However, in AL Physics, because of its simplicity, only Coulomb friction is considered.

Reference:
Wikipedia
http://en.wikipedia.org/wiki/Friction
and the link it refers to:
http://www.roymech.co.uk/Useful_Tables/Tribology/co_of_frict.htm