Linear Motion - Position Versus Time
Project Overview
Using real time data from satellites in orbit, students will use Excel to plot position vs.
time data to determine the average speed of the vessel. Furthermore, students will draw
motion diagrams, draw qualitative position vs. time graphs, describe the motion of
objects, and translate between these multiple representations.
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Student Learning Objectives
By the completion of this lesson, students will be able to:
1. Draw motion diagrams
2. Draw qualitative position vs. time graphs
3. Describe the motion of objects
4. Translate between motion diagrams, position vs. time graphs, and verbal
descriptions of motion
5. Collect position and time data from an on-line data source and/or digital movie
and/or simulation
6. Enter data into spread sheet and plot position vs. time
7. Analyze position vs. time graph to determine the velocity of object
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Procedure
After reading the Overview, students should proceed through the Content Materials in the
following order:
1. Introduction to Motion
2. Motion Diagrams
3. Position vs. Time Graphs
4. Translating Between Representations
5. Real World Motion
You may then want students to complete the Assessment.
Rather than make this too cookbook-like by providing worksheets to fill out, I
recommend that students collect data in their lab notebooks. They should follow the
procedures, making requisite assumptions as they go. You may want to have student
write up a more formal lab report if that fits your curriculum.
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Content Material
“Of all of the intellectual hurdles which the human mind has confronted and has
overcome in the last fifteen hundred years, the one which seems to me to have been the
most amazing in character and the most stupendous in the scope of its consequences is
the one relating to the problem of motion.” Herbert Butterfield in The Origins of Modern
Science (as quoted by Randall Knight in Five Easy Lessons)
We use many words to describe motion… location, position, distance, displacement,
speed, velocity, acceleration, deceleration, etc. These words have dictionary definitions,
more precise physics definitions, and personal definitions. By the end of this activity,
your personal definition should be closer to that of a physicist.
An underlying concept for all motion is that of coordinates. To identify the
location of your car keys, your best friend’s house, or a satellite
in orbit, you need to know “compared to what?” There are no
absolute coordinates, but there are some typical ones for
different uses. Your keys are usually located with reference to
your house or dorm layout (“in the laundry room”). Your
friend’s house is generally located by some regional street layout. A satellite in
orbit (like the Hubble telescope) is typically located with latitude, longitude and
altitude. It is true that your friend’s house and your keys could also be located
with latitude, longitude and altitude, but that probably wouldn’t be too useful.
One of the key skills you are to develop in this course is to be able to communicate
technical information with others. Communication that presents information in multiple
forms is usually better than using just words. So, you’ll practice using motion diagrams
and position vs. time graphs in addition to words. You will also practice translating
between the various representations.
Another important skill is the ability to use technical tools effectively. Towards that end,
you’ll collect live position data for a satellite using the internet. Alternatively, you might
use a movie of some real motion to collect data or you might use a simulation to collect
data. You will then use Microsoft Excel to analyze and display the data in tables, graphs
and equations.
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Assessment
Motion Diagrams
Draw motion diagrams for the following motions:
1. Moving toward the origin at a steady rate.
2. Moving away from the origin slowly then speeding up; then reversing directions,
moving quickly and slowing down.
3. Standing still for a few seconds, moving away slowly and steadily for a few more
seconds. Then, moving away twice as fast as before. Finally, moving back
toward the origin at a speed slower than the original speed.
Position vs. Time Graphs
Draw a position vs. time graph for the following motions:
1. Moving toward the origin at a steady rate.
2. Moving away from the origin slowly then speeding up; then reversing directions,
moving quickly and slowing down.
3. Standing still for a few seconds, moving away slowly and steadily for a few more
seconds. Then, moving away twice as fast as before. Finally, moving back
toward the origin at a speed slower than the original speed.
Translating between representations
Complete the other two representations* for each of the following:
1. Assuming the origin is the floor, drop a Super Ball. It falls, bounces off the floor
and returns to nearly the same height as it was dropped.
2. Consider this motion:
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position (m)
3. Consider this motion:
time (s)
* Words, motion diagram, and position vs. time graph.
Putting it all together
Create a complete model for your satellite. Your model should include a:
1. copy of the original data (from the database website),
2. Excel data table of time and position data,
3. verbal description of the motion,
4. motion diagram, and
5. Excel graph of motion with trendline and equation.
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Assessment Check Sheet
Motion Diagrams
# Excellent Adequate
1.
2.
3.
Inadequate
Comments
Position vs. Time Graphs
# Excellent Adequate Inadequate
1.
2.
3.
Comments
Translating between representations
# Excellent Adequate Inadequate
1.
2.
3.
Putting it all together
# Excellent Adequate
1.
2.
3.
4.
5.
Comments
Inadequate
Comments
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Links to Course Competencies
This lesson fits into the Maricopa Community College District’s PHY 111 course. For
the complete official course description, course competencies and topics, go to:
http://www.dist.maricopa.edu/curriculum/M-Z/026phy111.html
This RWLO addresses portions of competencies 1, 2 and 3 and is contained within topic
I:
PHY 111 Competencies
1. Effectively communicate qualitative and quantitative information orally and in
writing.
2. Explain the application of fundamental physical principles to various physical
phenomena.
3. Apply appropriate problem-solving techniques to practical and meaningful
problems using graphical, mathematical, and written modeling tools.
4. Work effectively in collaborative groups.
PHY 111 Outline
I.
II.
III.
IV.
V.
Linear Motion
Non-linear Motion
Forces and Momentum
Work, Energy Storage and Transfer
Properties of Matter
The Arizona Education Department is currently undergoing a review of the state-wide
science standards. You can access the standards here:
http://www.ade.state.az.us/standards/science/survey/sciencestandard.asp
National Science Education Standards (1995)
Center for Science, Mathematics, and Engineering Education
http://www.nap.edu/books/0309053269/html/index.html
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Supplementary Resources
Motion Diagrams, graphs, etc.:
http://www.rit.edu/~agysps/courses/311sclp/cl_wkshts_311/motiondiags&grfs.htm
Minds-On Physics 1-D kinematics:
http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/1DKinTOC.html
Science @ NASA (lots of cool stuff including satellite tracking tools):
http://science.nasa.gov/temp/StationLoc.html
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Recommendations
This activity is designed for the first semester of a two-semester algebra-based college
physics course. However, high school courses, one-semester conceptual courses, and/or
the first semester of the calculus-based sequence would likely find this useful.
Depending on how the course is structured, this could likely fit within the early
introduction to motion. We expect that students already have experience with creating
graphs and that they understand the concept of slope. To be successful, students also
need some facility with Microsoft Excel. They need to be able to enter data, create an XY (scatter) plot, add a trendline, and display the equation. If they don’t have prior
experience, this would serve as simple, yet rich, introduction to Excel. Depending on
student preparation, this activity will likely require between 90 and 150 minutes to
complete.
This RWLO was originally based on an activity created for CIESE which had students
tracking ships at sea, but the ship database site was taken down. While there was a workaround, the data mining required of students was too extensive and I believe they would
lose site of the main point of the lesson. Instead, we’ll use the tracking of satellites
(which also gives us an excuse to look at cool pictures like this):
This activity attempts to walk the line between
too much and not enough direction. College
students need to be weaned from a cookbook
approach to all activities. If you compare the
directions for this activity versus those from The
Stowaway Adventure, you’ll see that the role of
the student and that of the teacher are
significantly changed. In the middle school
version, the teacher is responsible for finding
appropriate ships on any given day and the
instructions are very explicit and step by step. In
this version, the student is given the responsibility
of finding an appropriate satellite and for
interpreting what it is they need to do. This is as
it should be.
In case there is difficulty accessing the real time data, you will find a folder for both the
Hubble and the space station, each with 5 data pages. Good luck!
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