What is the motion of a body when only the force of gravity is acting on it

When only the force of gravity acts on an object,
the situation is called "free fall".

The motion is uniformly accelerated.  The object falls
straight toward the center of the other object in whose
gravity it shares, and its speed increases at a constant
rate. 

When this happens on or near the surface of the Earth,
the rate is (9.8 meters per second greater) for each
second of falling.

True free-fall is never observed in daily life.  Whenever
we see an object falling, it is always falling through air,
which counteracts the force of gravity to a greater or
lesser degree, depending on the object's size, shape,
weight, surface texture, and speed through the air.