Unit 12 Investigation 2 DisplayingChangingMotion
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Displaying Changing Velocity
Contents
• Introduction
• Thinking About the Question
• Materials
• Safety
• Trial I : Matching Motion
• Trial II: Speeding Up?
• Trail III: Changing Direction?
• Technical Hints
• Analysis
• Further Investigations
Investigating Motion Introduction
Discovery question: When am I changing velocity or accelerating?
Cartoon of a generic runner (no female or male shown)
[cartoongenericrunner.jpg]
This activity will allow you see and analyze change in position over time in
graphical form.
Thinking About the Question
When am I changing velocity or accelerating?
Imagine you are a marine biologist. You want to track the movements of whales
in the ocean. What information about the movements of the whale would you
want to know? Where is the whale? What is the whale’s position? How fast is the
whale traveling? How does the motion of the whale relate to other moving
objects?
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Think about other professions. A racecar driver wants to know how fast they can
reach a certain speed? A baseball player wants to know how fast a pitcher
throws a fastball. What information about the movements of other objects in
motion would you want to know? Discuss these questions with your team and
write down some of your examples and questions to share with the class.
KWL strategy– state what you know and wonder about motion
[Answers: Student answers will vary. Possible answers may include the
following. Airline pilots wants to know the fastest speed they can travel crosscountry. A train passenger in Japan wants to know how fast a high-speed train
travels from one city to another.]
There is technology that helps scientists to answer questions about motion. Many
ships use sonar to find objects at the bottom of the ocean and to “view” objects,
like whales, as the ship draws near them. A motion sensor (also called an
ultrasonic detector) uses technology for a similar purpose. Refer to Technical
Hints to learn how a motion sensor works.
Observe the following graph.
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[changevelgraph.jpg] [Matthew, all graphs in both U12 activities should
have Position (m) on the Y-axis and not Distance (m). Also, all of the
graphs should have the same size in both investigations.]
This graph is the movement of a car on a 4 meter straight race track as displayed
by a motion sensor. What facts can you determine from the graph about the
motion of the car?
Observations – explanation of a motion graph.
[Answer: The car is starting three quarters of the way through the track. The car
moves backwards 1/2 meter and forwards 1/2 meter in a repeated pattern before
it moves 1.5 meters backwards. The car then moves 0.5 meter backwards three
times until it finally moves backwards 2 more meters. The driver never reaches
the end or starting line and must be very confused!]
Materials
• motion sensor [linked to Technical Hint Choosing the motion sensor]
• meter stick or tape measure
• masking tape
• stool or table (approximately waist high)
Safety
If more than one motion sensor is used in a classroom, separate each sensor by
at least two meters to prevent waves from one sensor from interfering with the
waves from another sensor.
Trial I
Matching Motion
1. Refer to Technical Hints to set up the walking track.
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Graph 1
[flattopgraph.jpg] [This should be available as an overlay during data collection]
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Graph 2
[cattopgraph.jpg] [This should be available as an overlay during data collection]
2. Look and compare the two motion graphs shown above. What similarities
and differences do you notice about the shape of the lines in the two
graphs?
Observations – explanations of visual graphical phenomenon
[Answer: Both graphs start and end at the same location. Both graphs move
around 2 meters at the beginning of the motion and backwards at the end of
the motion. Differences in the pattern occur at the top of the graph.]
3. Write a short description for Graph 1 that tells the story of the needed
movement. Be sure to include numerical information about the direction of
your motion, the speed of your motion, and your distance from the starting
point when changes in direction and speed occurred.
Prediction –verbalize and communicate a method to produce the desired
graphical display.
[Answer: Starting point is at 0.4 meter with no motion for 12 seconds and then
movement forward for around 2 meters. There is no motion for 20 seconds.
Around 40 seconds the motion is backwards for 10 seconds until the starting
point is reached. Finally there is no motion for 5 seconds.]
4. Write a short description for Graph 2 that tells the story of the needed
movement. Be sure to include numerical information about the direction of
your motion, the speed of your motion, and your distance from the starting
point when changes in direction and speed occurred.
Prediction –verbalize and communicate a method to produce the desired
graphical display.
[Answer: Starting point is at 0.5 meter with no motion for 5 seconds and then
movement forward for around 2 meters. It rests for a short amount of time and
moves forward quickly after two seconds and reverses direction quickly and
then rests for about 10 seconds. This motion is repeated again before
returning again to the starting point. Around 35 seconds the motion is
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backwards for 10 seconds until the starting point is reached. Finally, there is
no motion for 15 seconds.]
5. With your back to the motion sensor, try to reproduce Graph I from your
description. Refer to Technical Hints to run the motion sensor software.
Repeat until you capture the desired graph. Save the graph. Refer to
Technical Hints to save graphs.
Performance Assessment – use the motion sensor to produce a motion graph.
Matching Overlay needed. Position (0-4 meters) versus Time (0-60 seconds)
[Answer: Student performance will vary. How close to the overlay were the
students able to reproduce the graph?]
6. Compare the graph that you created with original Graph 1. List any
changes needed in your description to better reproduce the original graph.
Written Assessment – verbalize the method used to produce the desired motions.
[Answer: Student answers will vary.]
7. With your back to the sonar ranger, try to reproduce Graph 2 from your
description. Refer to Technical Hints to run the motion sensor software.
Repeat until you capture the desired graph. Save the graph. Refer to
Technical Hints to save graphs.
Performance Assessment – use the motion sensor to produce a motion graph.
Matching Overlay needed. Position (0-4 meters) versus Time (0-60 seconds)
[Answer: Student performance will vary. How close to the overlay were the
students able to reproduce the graph?]
8. Compare the graph that you created with original Graph 2. List any
changes needed in your description to better reproduce the original graph.
Written Assessment – verbalize the method used to produce the desired motions.
[Answer: Student answers will vary.]
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9. Describe the relationship between the change in speed needed and the
lean of the lines found in the ‘cat’s ears.’
Observations – explanation of a motion graph
[Answer: The cat’s ears are by far the fastest portion of the graph. The students need
to immediately change direction and move rapidly for a short amount of time.]
Trial II
Speeding Up?
1. Observe the graph.
[speedingupgraph.jpg] [This should be available as an overlay during data
collection]
2. Write a short description for the graph that tells the story of the needed
movement. Be sure to include numerical information about the direction of
your motion, the speed of your motion, and your distance from the starting
point when changes in direction and speed occurred.
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Prediction –verbalize and communicate a method to produce the desired
graphical display.
[Answer: Starting around 1.2 meters from the motion sensor, then no
motion occurs for 1 second. As no motion continues for 3 seconds and the
motion immediately starts moving backwards slowly for around 2.5
seconds and than speeds up for another 2 seconds and stops for 1
second.]
3. With your back to the sonar ranger, try to reproduce the graph from your
description. Refer to Technical Hints to run the motion sensor software.
Repeat until you capture the desired graph. Save the graph. Refer to
Technical Hints to save graphs.
Performance Assessment – use the motion sensor to produce a motion graph.
Matching Overlay needed. Position (0-4 meters) versus Time (0-60 seconds)
Graph II
[speedingupgraphlabeled.jpg]
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4. Now that you have experienced the needed changes in speed to
reproduce the graph, select the letters from the graph shown above to
identify the following motions. Write a short justification for each selection.
a) no movement [Answer: A,E – flat lines with no slope]
b) moving at same or constant speed [Answer: A, E, B, D – straight or
nearly straight lines]
c) changing speed [Answer: C – curved line that is constantly changing
speed]
d) increasing speed [Answer: C – curve gets steeper]
e) decreasing speed
[A writing box will allow both the letter selection and the justification fort
each motion.]
Conceptual probe – vague question with several possible answers which
the student must state a justification of their model
5. Based on your explanation of the graph, do you agree that a straight line
shows constant speed?
Written Assessment – verbalize the method used to produce the desired motions.
[Answer: Yes, the slope is the same at any location on the line.]
6. Why would changing speed, otherwise known as acceleration, be shown
as a curve on the graph?
Written Assessment – verbalize the method used to produce the desired motions.
[Answer: The slope is constantly changing. Lines drawn tangent to the curve at
different points on the curve would have different slopes.
Unit 12 Investigation 2 DisplayingChangingMotion
Tangent lines increase
in slope.
Trial III
Changing Direction?
1. Observe the graph.
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Unit 12 Investigation 2 DisplayingChangingMotion
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f
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b
[changingdirectiongraph.jpg]
Write a short description for the graph that tells the story of the needed
movement. Be sure to include numerical information about the direction of
your motion, the speed of your motion, and your distance from the starting
point when changes in direction and speed occurred.
Prediction –verbalize and communicate a method to produce the desired
graphical display.
[Answer: Starting at 3 meters there is no motion for one second. For nearly 2
seconds the motion is backwards and not constant. For 1.5 seconds there is
no motion and then there is movement forward for 2 seconds. Finally, the
motion is backwards rapidly that slows slightly at 1.5 seconds.]
2. With your back to the sonar ranger, try to reproduce Graph I from your
description. Refer to Technical Hints to run the motion sensor software.
Repeat until you capture the desired graph. Save the graph. Refer to
Technical Hints to save graphs.
Performance Assessment – use the motion sensor to produce a motion graph.
Matching Overlay needed. Position (0-4 meters) versus Time (0-60 seconds)
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[Answer: Student performance will vary. ]
3. Label your graph to show forward (f) motion and backward (b) motion.
How did the actual motions compare to your predictions? Explain any
differences.
Written Assessment – verbalize the method used to produce a desired
motion.
[Answer: See graph. How close to the overlay were the students able to
reproduce the graph?]
[changingdirectiongraphlabeled.jpg]
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4. Now that you have experienced the needed changes in speed to
reproduce the graph, select the letters from the graph shown above to
identify the following motions. Write a short justification for each selection.
a. no movement [Answers: A,C, E – flat line with no slope]
b. forward motion [Answer: D – positive slope]
c. backward motion [Answers: B, F – negative slope]
d. same or constant speed [Answers: A, C, E, flat lines with no speed]
e. changing speed [Answers; B, D, F – slight curves]
f. increasing speed [Answers: B, D – When tangent lines are drawn at
different locations on the curve, increasing slopes are visible for the
tangent lines.]
g. decreasing speed
[A writing box will allow both the letter selection and the justification fort
each motion.]
Conceptual probe – vague question with several possible answers which
the student must state a justification of their model
Technical Hints
• Choosing the motion sensor
• Learning about the motion sensor
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[bat.jpg]
Bats fly back and forth in a cave at night to find their food. While flying at night, a
bat emits squeaks that reflect off the walls of caves and flying insects. These
squeaks return to the bat’s nervous system and are used as clues to determine
the location and shape of the objects. The bat can tell where the next meal is and
when to avoid other objects.
A motion sensor (also called an ultrasonic detector) uses technology for a similar
purpose. A motion sensor uses a motion detector that sends out high frequency
sound waves to a target object and waits for the sound wave to come back. The
motion sensor measures the time needed for the wave to leave and return to the
detector. What is so unique about a motion sensor is that software can determine
and display the distance a wave covered based on the speed of sound in a
graph.
• Running motion sensor
• Saving graph
• Setting up walking track (need picture of a track with neutral student)
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This is my generic version (for reference only) [motionsensortrack.jpg].
See picture of boy provided. His picture needs to show more of the
track like the girl’s picture. Please use his picture just for the stance.
[boymotiontrack.jpg]
1. Find an open space around 1 meter wide and 5 meters long (possibly in a
hallway).
2. Using masking tape, mark off the straight-line distance with half-meter
divisions, starting at the motion sensor.
3. Place the motion sensor on a stool or table that is waist high. Align the
motion sensor with the tape.
• Creating a drawing
Analysis
1. What did you learn about changing motion in relationship to the movement of
your body? Was it difficult to reproduce the motion graphs?
KWL strategy– state what you learned about motion
[Answer: Student answers will vary. Acceleration or increasing speed or change in
direction is often hard to reproduce.]
2. How does the graphical display of the change in position over time relate to
change in speed?
Written Assessment – verbalize in mathematical terms the motion that was
produced.
[Answer: If the graph is a curve, the speed is changing and accelerating. If it is a
straight line there is no acceleration.]
3. How does the graphical display of the change in position over time relate to
change in direction?
Written Assessment – verbalize in mathematical terms the motion that was
produced.
[Differences between the slope sign shows the direction. Positive slope is forward and
negative slope is backwards motion.]
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4. Observe the following graph .
[plateaugraph.jpg]
Determine the speed between 25 and 30 seconds. Describe your method to
determine the speed.
Written Assessment – verbalize the method used to produce a desired
motion.
[The distance covered was 1.2 meters in 5 seconds. Since speed is change of
distance over time the speed is 1.2 meters/ 5 seconds or 0.24 m/s.]
5. Observe the following graph.
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[walkingpersongraphlabeled.jpg]
Is the student moving faster at A or B on the graph? Justify your answer.
Written Assessment – verbalize in mathematical terms the motion that was
produced.
[Answer: A The same amount of distance is covered in less time.]
Further Investigations
• Predict the position – time graph for the motion of a bouncing ball. Test the
prediction with a motion sensor.
Predictions – verbalize and communicate a method to produce the desired graphical
display
Performance Assessment – use the motion sensor to produce a motion graph.
Position (0-4 meters) versus Time (0-60 seconds)
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• Work with your team to create a motion graph of your own using the motion sensor.
This could include change in direction, starting position, and speed. Write down the
method that you used to make the graph. Have another team try to reproduce your
graph from the written description. Compare the graphs between the two teams.
Predictions – verbalize and communicate a method to produce the desired graphical
display
Performance Assessment – use the motion sensor to produce a motion graph.
Position (0-4 meters) versus Time (0-60 seconds)