Theoretical maximum velocity for a bullet?

Hope this helps.

http://www.frfrogspad.com/miscellb.htm

Highest Bullet Velocity

A shell from the Paris Gun reached a speed of 5,200 ft/s. That was using basic gun powder propellant. The M829A2 APFSDS round the M1A1 Abrams fires from it's 120mm main gun is slightly faster.

Then there was project HARP. A non-rocket space launch method based on a very large gun to fire the models to high altitudes and speeds (aka a space gun). If I got my math right they fired a shell at 11,810 fps.

As for small arms I do not know. I'll assume the limit will be based on the propellant used.

One has to remember that the rate of explosive expansion does not translate to the maximum achievable MV, providing burn can be achieved & pressure dealt with gas expansion from a larger area can be channeled resulting in Vs higher than the actual rate of explosive expansion. Other limitations such as pressure & counter pressure (form the gas in front of the bullet) are the enemy.

Without odd breach arrangements conventional powders lack the energy densities to perform much beyond 6,000fps though going over to solid, cast propelants allows high MVs such as the Ukrainian Vitiaz 125mm FSAPDS round reported to travel @ 6,700fps.

Experimental though fundamentally conventional guns, e.g. the 81.3mm/95 CARDE gun, have operated at 9,000+fps at normal atmospheric pressure, though when firing in a vaccum "convential" guns have more than doubled this (See August 2003 American Rifleman)

In response to Snowie's answer; I'm no physicist but I do have some understanding of Newton's third law. Once the projectile leaves the muzzle of a firearm it has achieved it's maximum velocity. In a vacuum like space it will retain that velocity until it either hits something or is influenced by another source such as gravity. It can't however accelerate it's velocity unless it is acted upon by an outside source such as, again, gravity.

Depends.

Speed of light, Lord that's funny stuff. Oh, wait. You weren't joking.

http://www.quarry.nildram.co.uk/highvel.htm

Basically the conclusion states that about 6000 fps is a "cap" on bullet velocities.

WOW...lol...Even an old man can learn something new every day..Good job folks

If you shot a bullet from outside the space station; in theory, it would gain velocity till it achieved speed just under that of the speed of light.