If an object is in equilibrium, does it have to be at rest?

From Newton's laws, we know that an object in equilibrium won't accelerate or decelerate in any direction, but this doesn't mean it is at rest! It may be moving (or even spinning) at a *constant speed*. A great example is people using parachutes - they're obviously falling and not at rest, but as air resistance and gravity are in equilibrium, they are no longer accelerating (if they cut their parachute, they would start accelerating pretty quickly!)

Mathematically, we can look at Newton's 2nd law, which can be written as F=ma. Equilibrium means that the total force on an object is 0, and thus it's acceleration is also 0, but doesn't say anything about speed!

An object can be in equilibrium and moving at a constant velocity. A spacecraft moving through the solar system will be moving at a constant velocity and will do so forever until an external force acts on it.