A graphical version of this slide is also available.

An object that is falling through a vacuum is subjected to only
one external force, the gravitational
force, expressed as the weight of the object. An object that is
moving only because of the action of gravity is said to be **free
falling** and its motion can be described by Newton's Second
Law of Motion. With algebra we can solve
for the **acceleration** (change of velocity) of the object
which is a constant
and equal to the gravitational acceleration. The mass, size, and
shape of the object are not a factor in describing the motion of the
object; a beach ball falls at the same rate as an airliner.
Knowing the acceleration,
we can predict the velocity and location of a free falling object at
any time by solving the equations of motion If the
object were falling through the atmosphere,
there would be an additional drag force
acting on the object and the physics
involved with describing the motion of the object would be more
complex.

For objects near the surface of the earth, the graviation acceleration (g) is a constant and equal to 9.8 meters per second squared. The velocity (V) is then equal to the acceleration (g) times the time. (The change in velocity from one time to another is acceleration (g) times the difference in time). The displacement distance (d) is equal to one half the accelereration times the square of the time. Here is a table of the accleration (meters per second squared), velocity (meters per second), and displacement (meters) at 1 second intervals.

Time = 0, Accel = 9.8, Velocity = 0.0, Distance = 0.0

Time = 1, Accel = 9.8, Velocity = 9.8, Distance = 4.9

Time = 2, Accel = 9.8, Velocity = 19.6, Distance = 19.6

Time = 3, Accel = 9.8, Velocity = 29.4, Distance = 44.1

Time = 4, Accel = 9.8, Velocity = 39.2, Distance = 78.4

Time = 5, Accel = 9.8, Velocity = 49.0, Distance = 122.5

Time = 6, Accel = 9.8, Velocity = 58.8, Distance = 176.4

Time = 7, Accel = 9.8, Velocity = 68.6, Distance = 240.1

Time = 8, Accel = 9.8, Velocity = 78.4, Distance = 313.6

Notice that the acceleration is a constant, the velocity increases linearly, and the location increases quadratically.

The remarkable observation that all free falling objects fall at
the same rate was first proposed by **Galileo,** nearly 400 years
ago. Galileo conducted experiments using a ball on an inclined plane
to determine the relationship between the time and distance traveled.
He found that the distance depended on the square of the time and
that the velocity increased as the ball moved down the incline. The
relationship was the same regardless of the mass of the ball used in
the experiment. The story that Galileo demonstrated his findings by
dropping two cannon balls off the Leaning Tower of Pisa is just a
legend. However, if the experiment had been attempted, he would
have observed that one ball hit before the other because falling
cannon balls are not actually free falling - they are subject to
air resistance and would fall at different
terminal velocities.

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*byTom
Benson
Please send suggestions/corrections to: benson@grc.nasa.gov *