Kurtis Foden
PHYS1410L 819
Rigel Cappallo
Motion in Free Fall
11 February 2016
Partner: Daniel Richter
Objective: To determine from the measurements the rate at which
the velocity of an object changes due to gravity.

Introduction:
If a body is acted upon by a net force, then that force causes the body to accelerate.
If the force is constant in magnitude, then the acceleration of the body will also be constant. A
body which is allowed to fall freely is acted upon by the force of gravitational attraction between
that body and the earth, and is directed toward the center of the earth. If the distance of the fall is
very much less than the earth’s radius then this gravitational force is essentially constant in
magnitude and the acceleration due to gravity (g) will be constant during the time of fall. We
ignore here a second force due to air resistance, which also acts on a falling body. However, for
smooth, dense bodies falling only a short distance, air resistance is very small. Its effect can be
ignored in the present experiment. In the first figure are shown curves representing the
relationships between displacement and time, and velocity and time (respectively) for a body
moving at constant acceleration. The acceleration is defined as the rate of change of velocity
with time.
a = (v-v
0
)/t
or v = v
0
+ at Equation 1
where “a” represents the acceleration of the body whose velocity changes from an initial value
“v
0
”to a final value “v” in the time interval “t”. From equation 1 we see that a plot of v v. t should
be a straight line if the acceleration is constant, as seen in equation 2. The slope of this line is
equal to the acceleration a. The average velocity of a body is defined as the total displacement (s)
travelled by the body divided by the time taken to travel that displacement.
v
avg
= s/t Equation 2
For uniformly accelerated motion the average velocity is simply the arithmetic mean of
the initial and final velocities (“v
0
“and “v”) over the time interval “t”
v
avg
= (v
0
+ v)/2 Equation 3
Furthermore, this average velocity is equal in magnitude to the actual, or instantaneous,
velocity midway during the time interval “t”, in other words, it equals the instantaneous velocity
at the instant of time “t”/2, as can be seen from figure 1, equation 2. Combining equations 1, 2,
and 3 we arrive at the following relationship between displacement and time:
s = v
0
t + 0.5at
2
Equation 4
From equation 4 we can see that a plot of “s” v. “t” should be a parabola if the