Here's why:
* Newton's First Law: An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
* Center of Mass: The center of mass represents the average position of all the mass in a system. It's as if all the mass were concentrated at that point.
* No External Force: If there's no external force, the total momentum of the system remains constant. Momentum is mass times velocity. Since the total momentum is constant, and the mass of the system is constant, the velocity of the center of mass must also be constant.
In simpler terms: Imagine a closed box with some marbles inside. If you shake the box, the marbles move around, but the overall center of the box doesn't change position. The same principle applies to a system of particles.
