Sloane Schneider
Acceleration
September 9, 2008
Laboratory Partners:
Taylor Whipple
Cory Wilkinson
Amy Kalal
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View Full DocumentPurpose:
The purpose of this laboratory is to compare three separate experiments in order to discover the
ways in which acceleration relates to position and velocity.
For this laboratory the motion sensor,
photogate, track, picket fence, a regular cart and a fan cart were used.
Sublist:
Experiment 1:
Using a free falling picket fence to calculate gravity
Experiment 2:
Calculating gravity with a photogate and cart down an almost frictionless track
Experiment 3:
Using a motion sensor and fan cart to calculate acceleration.
Theory:
There are three main equations found in the 2008 Physics Laboratory Manual that can be used
to solve for position, velocity, and acceleration.
Equation #1 will aid in solving for position, but is only
valid given a constant acceleration.
In the case of these experiments only a constant acceleration will be
used so Equation #1 is as follows:
Equation #1
x = x
0
+ v
0
t +
12
at
2
In order to solve for the velocity, which is the rate of change of position, the derivative of the position
equation relative to time is taken, giving Equation #2:
Equation #2
ddt
x = v = v
0
+ at
Finally, to solve for the acceleration of this object, the second derivative of Equation #1 (the first
derivative of Equation #2) is taken with respect to time.
Since these equations deal solely with objects
moving at a constant acceleration, this derivative will give you the equation for this constant acceleration.
Equation #3
=
=
d2dt2x
ddtv a
For two out of the three experiments done the acceleration of a free falling body was used.
This
acceleration equation is
a = g
when g = 9.80 m/s
2
.
Although g is always a positive number, we use
a = 
g
to show that the acceleration is in a downward motion.
When dealing with free falling bodies the
position versus time graph should be in the shape of a parabola.
When a downward direction is
considered negative the slope of the graph is negative and the velocity is negative.
For free falling
bodies the acceleration is negative (the object is falling down) mean the position versus time graph should
be concave down.
The slope of the velocity versus time graph is linear and equal to the constant
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 Spring '08
 SOWELL
 Physics, Derivative, Acceleration, Velocity, PHYSICS LABORATORY MANUAL, percent discrepancy

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