If there is only one object in the system, then with no external forces Newton’s Second Law says that its velocity will not change. Conservation of momentum also says that its momentum won’t change. If the momentum was zero, it will remain zero.

If you shoot a rifle or shotgun you are often told to hold the gun tightly against your shoulder. What’s the physics explanation for this admonition? When the gun is fired the bullet’s momentum changes. Its new momentum is in the forward direction. So, according to the law of conservation of momentum the gun must gain momentum in the opposite direction. It will recoil. If the gun isn’t held tightly to your shoulder its mass is relatively small, and so its recoil velocity will be large. When it hits your shoulder it could cause injury. If, on the other hand, the rifle is tight against your shoulder, then the mass is the mass of the rifle and your body. The recoil velocity will be much smaller.