Motion in Free-Fall
Objective: The objective of this Lab is to examine the motion of a body falling freely under
attraction, and then to determine from the measured rate at which the velocity changes with time
acceleration due to gravity (g).
Introduction:
Our task in this experiment was to examine the motion of a body falling freely under
gravitational attraction. 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 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 towards the center of the Earth. If the
distance of the fall is smaller than the earths radius than this gravitational force is essentially
constant during the time of the fall. We can ignore a second force due to air resistance, because
air resistance is very small. The rate of change is defined as the rate of change velocity with time,
so our first equation is
a
=
v
−
v
0/t (equation 1), in this equation “a” represents acceleration
whose velocity changes from initial value v0 to a final value v. If the acceleration in this equation
is constant than we can expect a straight line for the plot of v-vs-t, the slope of this line is equal
to acceleration
a
. The average velocity of a body is defined as the total displacement (s)
travelled by the time taken to travel that displacement, and that equation is
´
v
=
s
t
(equation 2).
To find the uniformly accelerated motion the average velocity is the arithmetic mean of the initial
and final velocity (v0 and v) over the time interval, so our equation is
´
v
=
v
0
+
v
2
(equation 3),
this average velocity is equal in magnitude to the instantaneous velocity midway during the time
interval, when we combine our equation 1,2, and three we get the following relationship between
displacement and time,
s
=
v
0
t
+
1
2
at
2
(equation 4), a plot of equation 4 would result in a
parabola if the acceleration is constant. The slope of the parabolic curve at any given instant of
time is equal to the velocity of the body at that time. So, to find the instantaneous velocity of the
velocity at any instant can be determined by drawing a tangent line to the displacement time
curve at the corresponding instant of time and measuring its slope. These equations are going to
be used to experiment the motion of an object falling freely under gravitational attraction, will be

studied by the by measuring its position at various instants of time during the fall. By plotting the