The statement that if there is no unbalanced force acting on an object, then it must be moving with a constant velocity is derived from Newton's first law of motion, also known as the law of inertia.
According to Newton's first law, an object at rest will remain at rest, and an object in motion will continue moving in a straight line with a constant velocity, unless acted upon by an external force. This principle is often summarized as "an object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction, unless acted upon by an unbalanced force."
When there is no unbalanced force acting on an object, it means that the forces acting on the object are balanced, resulting in a net force of zero. In this situation, the object will either remain at rest if it was initially at rest or continue moving in a straight line with the same velocity if it was already in motion.
The absence of an unbalanced force means that there is no force to cause a change in the object's motion. Without a net force, there is no acceleration, and therefore the object's velocity remains constant. This is consistent with the principle of inertia stated in Newton's first law.
It's important to note that this statement holds true in the absence of other factors such as friction or other external influences. In reality, objects in motion are often subject to various forces and may experience changes in velocity due to factors like friction, air resistance, or other interactions with the environment. However, in the idealized scenario where these factors are negligible, the statement holds true.