Lab 2 Report PHY 111
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Dec 6, 2023
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PHY 111
6/3/2023
Lab 2 Constant Acceleration Motion
Lab Purpose
The purpose of this lab is to analyze the motion of two different objects. In this lab, we analyzed
the positions, velocities, and accelerations of the two objects for any given moment in time.
Throughout the lab, we gathered data to create position vs. time and velocity vs. time graphs and
used those graphs to determine kinematic equations. This lab not only helps determine the
velocity approximations of two objects but also determines the position of the objects at a certain
time using the data collected.
Materials
The materials included a printer, paper, ruler, pen or pencil, tape, and scissors.
Procedure
First, Tape 1 and both sections of Tape 2 were printed and cut out to create three separate tapes.
After cut out, both section one and section two of Tape 2 were taped together to create one
continuous tape. After that, a ruler was used to measure positions of the object for both Tape 1
and Tape 2 at each 0.1 second interval as indicated by the dots relative to zero. Each data point
was recorded in two separate data tables for Tape 1 and Tape 2. Once all the data was collected
in a data table in Excel, the data was plotted into a graph for further analysis.
Photograph(s) of Experiment
Data
Tape 1:
Time (seconds)
Position (cm)
Velocity (cm/s)
Acceleration
(cm/s/s)
0.1
0.8
0.2
3.1
24
0.3
5.6
24.5
-2.5
0.4
8.0
23.5
12.5
0.5
10.3
27
15
0.6
13.4
26.5
-32.5
0.7
15.6
20.5
-35
0.8
17.5
19.5
0
0.9
19.5
20.5
2.5
1.0
21.6
20
-5
1.1
23.5
19.5
1.2
25.5
Tape 2:
Time (seconds)
Position (cm)
Velocity (cm/s)
Acceleration
(cm/s/s)
0.1
0.8
0.2
1.1
8
0.3
2.4
16.5
80
0.4
4.4
24
75
0.5
7.2
31.5
82.5
0.6
10.7
40.5
85
0.7
15.3
48.5
72.5
0.8
20.4
55
65
0.9
26.3
61.5
75
1.0
32.7
70
92.5
1.1
40.3
80
1.2
48.7
Calculations and Graphs
X= Position (cm) Y= Velocity (cm/s) t= Time (seconds)
Velocity (cm/s)
Acceleration (cm/s/s)
=(X
₃
-X
₁
) / (t
₃
- t
₁
)
(Y
₃
- Y
₁
) / (t
₃
- t
₁
)
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Results
For the position versus time graph for tape one, the object is moving forward at a constant speed
indicated from the linear, vertical line that the data forms. For the position versus time graph for
tape two, the object is moving forward at a high speed and is speeding up at a changing velocity.
This is indicated from the exponential equation given for the graph and its curved, parabolic
shape. For the velocity versus time graph for tape one, the object is moving forward but since the
slope is negative, the object is decelerating. For the velocity versus time graph for tape two, the
object is accelerating forward at a constant rate indicated by the linear, vertical line and the
positive slope.
Conclusion
Background-
In this lab, we focused on acceleration and velocity and how both of these
concepts helped us determine the position of an object at a certain time but how fast an object
was moving and in which direction. Acceleration is the rate at which velocity changes with time,
in terms of both speed and direction. Acceleration has both a magnitude and a direction and is
defined as the change in the velocity vector in a time interval, divided by the time interval. On
the other hand, velocity is a quantity that designates how fast and in what direction a point is
moving.
Interpretation of Results-
From Tape 1 position versus time graph, the slope is positive and the
line is straight and vertical. This means that the velocity is moving forward at a constant speed.
From the Tape 1 velocity versus time graph, the slope is negative and the way the points were
spread out on the graph indicates that the acceleration was decelerating forward but at a changing
velocity. Even though the line of best fit was a linear line, the points were spread out. From the
Tape 2 position versus time graph, the slope is positive but the graph itself is an exponential
graph. Since the slope is positive, the object is moving forward at a changing velocity and is
speeding up. From the Tape 2 velocity versus time graph, the slope is positive and the line is
linear and vertical. The object is accelerating forward at a constant rate.
Qualitative Discussion-
From examining the strips, I expected Tape one to have a linear and
positive slope for both the position and time graph as well as the velocity and time graph.
Surprisingly, the velocity versus time graph had a negative slope and was not linear. After
examining Tape two, I expected the graph to be exponential and have a curve for both graphs
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since the dots were spaced out unequally. However even though the position versus time graph
was exponential, the velocity versus time graph was linear.
Sources of Error-
In my experiment, I could have measured the position of the dots on the tapes
incorrectly. The ruler that I had used measured in mm so it was difficult to exactly measure the
position of each dot. Furthermore, since I converted my units from mm to cm, I may have
incorrectly rounded the decimal points which would have affected my results for the lab.
Analysis Questions Response
1.
2. Velocity is determined by the slope of the time-position graph. Since the slope of the
time-position graph is 22.678x, the slope would be 22.678 cm/s. If not given the equation, the
slope could be determined by choosing two plots on the graph and using the rise over run method
with those points.
3. Acceleration is determined by the slope of the time-velocity graph. Since the slope of the
time-velocity graph is 78.019x, the acceleration would be 78.019 cm/s/s. If not given the
equation, the slope could be determined by choosing two plots on the graph and using the rise
over run method with those points.
References
Encyclopædia Britannica, inc. (n.d.).
Acceleration
. Encyclopædia Britannica.
https://www.britannica.com/science/acceleration
Encyclopædia Britannica, inc. (2023, May 6).
Velocity
. Encyclopædia Britannica.
https://www.britannica.com/science/velocity
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