What is the state of an object accelerating due to the force of gravity alone?

Its state is in uniformly accelerated motion

Explanation:

When an object is acted upon the force of gravity only, we said that the object is in free fall.

According to Newton's second law of motion:

where F is the net force on an object, m is its mass, a its acceleration, when the net force on an object (F) is non-zero, than the object accelerates (because a is non-zero), so the object is in accelerated motion.

In case of free fall, the rate of acceleration of the object is equal to , the acceleration due to gravity, and it is constant. So, the object is moving by uniformly accelerated motion.