## College Physics (4th Edition)

The momentum of the bullet when it emerges from the muzzle is equal to the $Force\times Time$. If the barrel is shorter, the bullet emerges from the barrel after a shorter time. Thus the force is exerted on the bullet for a shorter time, which means that the bullet has a smaller momentum when it emerges from the barrel. Since the muzzle speed is the momentum divided by the mass of the bullet, the muzzle speed is smaller when the barrel is shorter.