Equilibrium and Newton's First Law

Newton's first law says an object's velocity stays constant unless a net force acts on it. Force doesn't cause motion, it causes changes in motion. A puck on frictionless ice has no net force once it's moving, so there's nothing to speed it up, slow it down, or turn it. It just keeps going, forever, at the same speed in the same direction. That's not a special trick of ice, it's what every object would do if you removed all net forces.

The mechanism is vectors. Net force equals mass times acceleration, so zero net force means zero acceleration. Acceleration is the rate of change of the velocity vector, both its magnitude and direction. If acceleration is zero, neither can change. That's why equilibrium includes two very different-looking situations: an object sitting still, and an object sailing along at constant speed in a straight line. Both have zero acceleration, so both count. People often reach for 'at rest' as the definition of equilibrium, but equilibrium is really a statement about force and acceleration, not about speed.

Equilibrium problems usually hand you an object held in place by several forces at angles, like a sign hanging from two cables, and ask you to find unknown tensions. You break every force into x and y components, then set each sum to zero separately, giving two equations you solve together. This same component method carries forward into every later topic in dynamics, where net force is no longer zero and you use the same component equations to find acceleration instead.