Free Fall motion
One-dimensional motion...
A free-falling object is an object that is falling under the influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall.

Free fall History
From Aristotle to Galileo.
The teachings of the great ancient wise Aristotle stating that heavy objects fall faster than light ones were accepted until the XVI Century. We know that if we drop a hammer and a feather or a sheet of paper from the same height, the hammer will reach first the ground. If we crumple the paper giving it a ball shape it is observed that both objects will reach the ground almost at the same time. It was the famous Italian physicist Galileo Galilei who refuted Aristotle's idea stating that, in absence of air resistance all objects fall with the same uniform acceleration. But Galileo didn't have a machine to create vacuum for sucking the air; the first pneumatic machine able to do this was invented afterwards, by the year 1650. He did not have watches exactly enough nor high speed photo cameras either. However, he cleverly proved his hypothesis using inclined planes getting a slower movement which could be measured with the rudimentary watches of that age. The slope of the planes could be increased gradually until reaching almost a vertical position allowing him to predict behavior of objects in free fall.
source: http://www.jfinternational.com/ph/free-fall.html
Free fall motion of objects exist endlessly. Millions of years ago, when meteors fell into the Earth's surface, they experienced free fall motion. The velocity of the meteors increased by 9.8 meters per second per sec.
It is the reason why small rock from space can damage hundreds of kilometers of land and ocean when it enters and impacts earth's surface .

Legend:
Vf=Final Velocity
Vi=Initial Velocity
G=Gravity (9.8 m/s/s)
T=Time
∆y=Displacement
Kinematic Equations for Free fall motion

You might think that since just about everything we observe falling is falling through the air, that "physics free fall" must be a pretty useless idea in practice. Not so! Any falling object's motion is at least approximately free fall as long as:
... it is relatively heavy compared to its size. (Dropping a ball, as in the picture at right, or jumping off a chair, is a free-fall motion, but dropping an unfolded piece of paper, or the motion of a dust particle floating in the air, is not. If you crumble the paper into a "paper wad", however, its motion is approximately free fall.
... it falls for a relatively short time. (If you jump off a chair, you are in free fall. After you have jumped out of an airplane and fallen for several seconds, you are not in free fall, since air resistance is now a factor in your motion.)
... it is moving relatively slowly. (If you drop a ball or throw it down its motion will be free fall. If you shoot it out of a cannon, its motion won't be free fall.)
You should also note that an object doesn't have to be falling to be in free fall - if you throw a ball upward its motion is still considered to be free fall, since it is moving under the influence of gravity.
Source: http://www.batesville.k12.in.us/physics/phynet/mechanics/kinematics/FreeFallIntro.html
Graphs of how the position, velocity, and acceleration of objects under free fall motion change in time follow.
Figure 2.3: Free fall acceleration
Figure 2.4: Free fall velocity
Figure 2.5: Free fall position


