Nice question, but I can only get a little start on the answer.
For friction in fluids (air, water etc.) the answers to your question are rather well understood. There the frictional force is proportional to the velocity for small velocities. That proportionality breaks down when the velocity becomes larger. In particular, it breaks down (and the drag goes up more rapidly) when something called the Reynolds’ number becomes large. It’s tough to describe that in a brief answer, but basically it keeps track of whether the momentum from the object moving through the fluid has time to diffuse away through the fluid before the object moves on to a new position. If you want more info, you can use Google or write back to us on that.
For solid-on-solid friction, described by a ’friction coefficient’, the friction force is pretty nearly independent of relative velocity for some range of relative velocity. At very low relative velocity, the friction tends to go up because there’s time for regions to stick together. I don’t know the general rules for how the friction changes at high relative velocity, and I suspect that whether it goes up or down depends a lot on the materials. Maybe a key word you could use to search for more information is ’tribology’. Perhaps the most important point to get is that solid-on-solid friction is a really complicated phenomenon, and the simple approximate rule F=mu*N used for it in elementary mechanics courses has no fundamental justification, even though it often works pretty well.
(published on 10/22/2007)