[camacazio]

The net force on the moving object is friction. I defined it as exactly that when I said F=ma=ngm. There is no other force on the system. After rereading your post a couple times, I think what you're trying to say is that I'm not modeling some sort of thrusting power of this object moving near the speed of light. I don't care about how it got to this speed. I don't even care why it's on earth, or how it found a run way long enough to slide along for any decent amount of time. All I care about is that it's coasting, and there is a linear force slowing it down--that being what is causing an expansion. This same equation I have come up with could be easily modified for when it accellerates to a certain speed, instead of a negative accelleration for slowing it down. In the end, as I stated above, all I want is a linear accelleration such that I can equate it to ma and also use it in a simple linear velocity equation. Friction in the macroscopic approximation gives an excellent and simple form for this, and that's why I use it. Typically special relativity avoids accelleration because it ventures into general relativity, so most things in special relativity ignore how and why something is moving near the speed of light. As long as I don't jump into the reference frame of this object that I'm modeling expansion of, I should be in the clear.