For quick results, try one of the classroomready activities in this guide!

Important information

This guide applies to all TI graphing calculators that can be used with the
CBR 2 motion detector (see page 2); therefore, you may find that some
of the menu names do not match exactly those on your calculator.
When setting up activities, ensure that the CBR 2 motion detector is securely anchored and that the cord cannot be tripped over. Always exit the EasyData App using the Quit option. The EasyData App performs a proper shutdown of the CBR 2 motion detector when you choose Quit. This ensures that the CBR 2 motion detector is properly initialized for the next time you use it. Always disconnect the CBR 2 motion detector from the calculator before storing it. EasyData is launched automatically when the unit-to-CBR 2 cable is connected from a TI-84 Plus or TI-84 Plus Silver Edition graphing calculator to a CBR 2 motion detector.
Hints for effective data collection

Getting better samples

How does the CBR 2 sonic motion detector work?
Understanding how a sonic motion detector works can help you get better data plots. The motion detector sends out an ultrasonic pulse and then measures how long it takes for that pulse to return after bouncing off the closest object. The CBR 2 motion detector, like any sonic motion detector, measures the time interval between transmitting the ultrasonic pulse and the first returned echo, but the CBR 2 motion detector has a built-in microprocessor that does much more. When the data is collected, the CBR 2 motion detector calculates the distance of the object from the CBR 2 motion detector using a speed-of-sound calculation. Then it computes the first and second derivatives of the distance data with respect to time to obtain velocity and acceleration data. It stores these measurements in lists.

Object size

Using a small object at a far distance from the CBR 2 motion detector decreases the chances of an accurate reading. For example, at 5 meters, you are much more likely to detect a soccer ball than a ping-pong ball.

Minimum range

When the CBR 2 motion detector sends out a pulse, the pulse hits the object, bounces back, and is received by the CBR 2 motion detector. If an object is closer than 15 centimeters (about six inches), consecutive pulses may overlap and be misidentified by the CBR 2 motion detector. The plot would be inaccurate, so position the CBR 2 motion detector at least 15 centimeters away from the object.

Maximum range

As the pulse travels through the air, it loses its strength. After about 12 meters (6 meters on the trip to the object and 6 meters on the trip back to the CBR 2 motion detector), the return echo may be too weak to be reliably detected by the CBR 2 motion detector. This limits the typical reliably effective distance from the CBR 2 motion detector to the object to less than 6 meters (about 20 feet).

Sensitivity switch

The sensitivity switch has two modesTrack and Normal. The Track mode is intended for activities using dynamics tracks and carts; the Normal mode is intended for all other activities, such as, walking, ball toss, bouncing ball, pendulum, etc.

Track Normal

If you are getting lots of extra noise in your data, the sensitivity switch may be in the Normal mode. Moving the sensitivity switch to the Track position, will reduce the sensitivity of the sensor and may produce better data.

The clear zone

(cont.)
The path of the CBR 2 motion detector beam is not a narrow, pencil-like beam, but fans out in all directions up to 15 from center in a 30 cone-shaped beam. To avoid interference from other objects in the vicinity, try to establish a clear zone in the path of the CBR 2 motion detector beam. This helps ensure that objects other than the target do not get recorded by the CBR 2 motion detector. The CBR 2 motion detector records the closest object in the clear zone.

15 centimeters

Reflective surfaces
Some surfaces reflect pulses better than others. For example, you might see better results with a relatively hard, smooth surfaced ball than with a tennis ball. Conversely, samples taken in a room filled with hard, reflective surfaces are more likely to show stray data points. Measurements of irregular surfaces (such as a toy car or a student holding a calculator while walking) may appear uneven. A Distance-Time plot of a nonmoving object may have small differences in the calculated distance values. If any of these values map to a different pixel, the expected flat line may show occasional blips. The Velocity-Time plot may appear even more jagged, because the change in distance between any two points over time is, by definition, velocity.

EasyData settings

Setup data collection for Time Graph
Experiment length is the total time in seconds to complete all sampling. Its determined by the number of samples multiplied by the sample interval. Enter a number between 0.05 (for very fast moving objects) and 0.5 seconds (for very slow moving objects). Note: See To set up the calculator for data collection on page 12 for detailed information about how to change settings.

Menu name Description

Measures time between samples in seconds. Total number of samples to collect. Length of the experiment in seconds.

Default setting

Sample Interval Number of Samples Experiment Length

Starting and stopping

To start sampling, select Start (press q). Sampling will automatically stop when the number of samples set in the Time Graph Settings menu is reached. The CBR 2 motion detector will then display a graph of the sampled data on the graphing calculator. To stop sampling before it automatically stops, select Stop (press and hold q) at any time during the sampling process. When sampling stops, a graph of the sampled data is displayed.
Noisewhat is it and how do you get rid of it?
When the CBR 2 motion detector receives signals reflected from objects other than the primary target, the plot shows erratic data points (noise spikes) that do not conform to the general pattern of the plot. To minimize noise:
Make sure the CBR 2 motion detector is pointed directly at the target. Try adjusting the sensor head while viewing live data on the home-screen meter. Make sure the reading you receive is appropriate before starting an activity or experiment. Try to sample in a clutter-free space (see the clear zone drawing on page 7). Choose a larger, more reflective object or move the object closer to the CBR 2 (but farther than 15 centimeters). When using more than one CBR 2 motion detector in a room, one group should complete a sample before the next group begins their sample. Try moving the sensitivity switch to the Track position to reduce the sensitivity of the sensor.

Speed of sound

The approximate distance to the object is calculated by assuming a nominal speed of sound. However, actual speed of sound varies with several factors, most notably the air temperature. The CBR 2 motion detector has a built-in temperature sensor to automatically compensate for changes in the speed of sound due to the temperature of the surrounding air. The temperature conversion from 0 to 40 Celsius, at standard pressure, is fairly linear at about +0.6 meters/second per degree Celsius. The speed of sound increases from about 331 meters/second at 0 Celsius to about 355 meters/second at 40 Celsius. These speeds assume a relative humidity of 35% (dry air). When using the EasyData App with the CBR 2 motion detector, this temperature compensation will take place when collecting motion data. The sensor is located underneath the holes on the back of the CBR 2 motion detector; therefore, when collecting data, do not cover these holes with something that is of a different temperature from the surrounding ambient temperature.

You may want to have your students hold a large book in front of them as they walk in front of the CBR 2 motion detector. This will produce better graphs because it smoothes out the motion.
This experiment may be the first time your students use the CBR 2 motion detector. A little coaching on its use now will save time later in the year as the CBR 2 motion detector is used in many experiments. The following are hints for effective use of the CBR 2 motion detector:

Typical plots

In using the CBR 2 motion detector, it is important to realize that the ultra sound is emitted in a cone about 30 wide. Anything within the cone of ultrasound can cause a reflection and possibly an accidental measurement. A common problem in using motion detectors is getting unintentional reflections from a desk or chair in the room. Often unintended reflections can be minimized by tilting the CBR 2 motion detector slightly. If you begin with a velocity or acceleration graph and obtain a confusing display, switch back to a distance graph to see if it makes sense. If not, the CBR 2 motion detector may not be properly targeting the target. The CBR 2 motion detector does not properly detect objects closer than 15 cm. The maximum range is about 6 m, but stray objects in the wide detection cone can be problematic at this distance.

Distance vs. Time

Matching Distance vs. Time

Answers to questions

9. The slope of the portion of the graph corresponding to movement is greater for the faster trial. Results will probably vary between groups as they may walk at different rates. Walking towards the motion detector will produce a negative slope. While walking away from the motion detector will produce a positive slope. 12. Note that the slope is close to zero (if not zero) when standing still. The slope should be zero, but expect small variation due to the variation in collected data.
2000 VERNIER SOFTWARE & TECHNOLOGY

linear

Graphs made using a CBR 2 motion detector can be used to study motion. In this experiment, you will use a CBR 2 motion detector to make graphs of your own motion.

Objectives

In this experiment, you will:
use a motion detector to measure distance and velocity produce graphs of your motion analyze the graphs you produce
Data collection: Distance vs. Time Graphs
Place a CBR 2 motion detector to a tabletop facing an area free of furniture and other
objects. The CBR 2 motion detector should be at a height of about 15 centimeters above your waist level.
walk back and forth in front of the CBR 2 motion detector
Use short strips of masking tape on the floor to mark the 1-m, 2-m, 3-m, and 4-m
distances from the CBR 2 motion detector.
Connect the CBR 2 motion detector to the calculator using an appropriate cable (see
below) and firmly press in the cable ends.
If TI-83 Plus, use an I/O unit-to-unit cable If TI-84 Plus, use a Standard-B to Mini-A USB cable (unit-to-CBR 2)
On the calculator, press and select EasyData to launch the EasyData App.
Note: EasyData will launch automatically if the CBR 2 motion detector is connected to a TI-84 Plus using a unit-to-CBR 2 cable.
Activity 1Graphing your motion (cont.)
To set up the calculator for data collection:
a. b. Select Setup (press p) to open the Setup menu. Press 2 to select 2: Time Graph to open the Time Graph Settings screen. Select Edit (press q) to open the Sample Interval dialog window. Enter 0.1 to set the time between samples to 1/10 second. Select Next (press q) to advance to the Number of Samples dialog window. Enter 50 to set the number of samples to collect. The experiment length will be 5 seconds (number of samples multiplied by the sample interval). g. h. Select Next (press q) to display a summary of the new settings. Select OK (press s) to return to the main screen.

c. d. e. f.

Explore making distance vs. time graphs.
a. b. c. d. Stand at the 1.0-m mark, facing away from the CBR 2 motion detector. Signal your partner to select Start (press p). Slowly walk to the 2.5-m mark and stop. When data collection ends, a graph plot is displayed.
e. f. Sketch your graph on the empty graph provided. Pick two points on the graph and determine the slope from the x and y-coordinates. Point 1:________ Point 2: ________ Slope:___________ g. Select Main (press r) to return to the main screen.

Repeat Step 6, this time standing on the 2.5m-mark and walk
towards the 1.0m-mark. One time walking slowly, and again walking more quickly. Point 1:________ Point 2: ________ Slope:___________
Sketch your new plots on the empty graph provided. Describe the differences between your graphs (step 6e and step 8)
___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________
Repeat Step 6, while standing still on the 2.5m-mark. Sketch your new plot on the empty graph provided. Calculate an approximate slope for all your graphs.
Activity 2Match the graph
Function explored: linear Distance Match introduces the real-world concepts of distance and timeor more precisely, the concept of distance versus time. In Explorations, students are asked to convert their rate of walking in meters per second to kilometers per hours. Once they have mastered the Distance-Time match, challenge your students to a Velocity-Time match.

Typical answers

1. time (from start of sample); seconds; 1 second; distance (from the CBR 2 motion detector to the object); meters; 1 meter 2. the y-intercept represents the starting distance 3. varies by student 4. backward (increase the distance between the CBR 2 motion detector and the object) 5. forward (decrease the distance between the CBR 2 motion detector and the object) 6. stand still; zero slope requires no change in y (distance) 7. varies by graph; @y3.3 8. varies by graph; @y1 9. the segment with the greatest slope (positive or negative) 10. this is a trick questionthe flat segment, because you dont move at all! 11. walking speed; when to change direction and/or speed 12. speed (or velocity) 13. varies by graph (example: 1.5 meters in 3 seconds) 14. varies by graph; example: 0.5 meters1 second example: (0.5 meters 1 second) Q (60 seconds 1 minute) = 30 meters minute example: (30 meters 1 minute) Q (60 minutes 1 hour) = 1800 meters hour example: (1800 meters 1 hour) Q (1 kilometer 1000 meters) = 1.8 kilometers hour. Have students compare this last number to the velocity of a vehicle, say 96 kilometers hour (60 miles per hour). 15. varies by graph; sum of the @y for each line segment.
calculator (see page 2 for available models) CBR 2 motion detector unit-to-CBR 2 or I/O unit-to-unit cable EasyData application

Trial 2 2.02 3.07

Trial 3 2.00 2.82

Average 2.00 2.90

1.97 2.80

parabolic
You have been familiar with playgrounds and slides since you were a small child. The force of gravity pulls you down a slide. The force of friction slows you down. In the first part of this experiment, you will use a CBR 2 motion detector to determine your speed or velocity going down a playground slide. In the second part, you will experiment with different ways to increase your speed going down the slide.
use a CBR 2 motion detector to determine your speed going down a slide experiment with ways to increase your speed going down the slide explain your results
Data collection, Part 1, Sliding Speed
a. b. Select Setup (press p) to open the Setup menu. Press 2 to select 2: Time Graph to open the Time Graph Settings screen.
Activity 3A Speedy slide (cont.)
c. d. e. f. Select Edit (press q) to open the Sample Interval dialog window. Enter 0.2 to set the time between samples in seconds. Select Next (press q) to advance to the Number of Samples dialog window. Enter 25 to set the number of samples. Data collection will last for 5 seconds.
Select Next (press q) to display a summary of the new settings. Select OK (press s) to return to the main screen.
Take your preliminary data-collection positions.
a. b. One member of the group should first go up the slide steps and sit at the top of the slide. A second person, while holding the CBR 2 motion detector, should go high enough on the slide steps to hold the CBR 2 motion detector behind the person who will slide. The third person should stand on the ground next to the slide, while holding the calculator and interface.
Take your final data-collection positions.
a. b. c. The slider, while holding on, should move forward enough to allow a 15-cm distance between his or her back and the CBR 2 motion detector. The person holding the CBR 2 motion detector should hold the CBR 2 motion detector steady and aim it at the sliders backside. The person holding the calculator and interface should move to a comfortable position that does not cause a pull on the CBR 2 motion detector cable.

Collect data.

a. b. c. Select Start (press q) to begin data collection. The slider should begin to slide as soon as a clicking is heard. When data collection is done for this trial, the person with the CBR 2 motion detector should come down to the ground. Caution: No student should attempt to pass another person while he or she is on the steps.

Determine the sliders speed.
a. b. c. After data collection stops and a graph of distance versus time is displayed, select Plots (press p). Press 2 to select 2: Vel vs Time to display velocity versus time.
Use ~ to examine data points along the graph. As you move the cursor right and left, the time (X) and velocity (Y) values of each data point are displayed above the graph. The highest point on the graph corresponds to the highest speed of the slider. Record this highest speed in the Data table. Round to the nearest 0.01 m/s. (In the example to the right, the highest speed is 2.00 m/s.) Select Main (press r) to return to the main screen.
Repeat Steps 47 two more times.
Data collection, Part 2, A Speedier Slide
Name __________________________________
Design a plan to increase the sliders speed. a. b. c. Try out some ideas for increasing the sliders speed. You may not coat the slide with anything that must be washed off. Decide on a plan to best increase the sliders speed. Describe your plan in the Speedier Slide Plan section below.
Test your plan using Part 1, Steps 48.

Speedier Slide Plan

Trial 2

Trial 3

Average

Data processing

1. Calculate the average speed for your three trials in Part 1. Record the average in the space provided in the Data table. Calculate and record the average speed for Part 2.
Subtract your Part 1 average speed from your Part 2 average speed to determine how much your team improved its speed.
What methods did other groups use to improve their speeds?
4. Which of the methods worked best? Explain why it worked best.
If you could increase the height of the slide, how would the sliders speed be affected?
If a stone was dropped from the top of the slide at the same time a similar stone was rolled down the slide, which stone would reach the ground first? Explain.
What is the purpose of the level portion at the bottom of many slides?

Activity 4Bouncing ball

Function explored: parabolic Real-world concepts such as free-falling and bouncing objects, gravity, and constant acceleration are examples of parabolic functions. This activity investigates the values of height, time, and the coefficient A in the quadratic equation, Y = A(X H) 2 + K, which describes the behavior of a bouncing ball.

On the Home screen, store the value you recorded in question 5 for the height in
variable K; store the corresponding time in variable H; store 1 in variable A. For example: Press 4 v t K , 2.5 v t H , 1 v t A to set K=4, H=2.5, and A=1.
Press to display the graph. Answer questions 6 and 7. Try A = 2, 0, 1. Complete the first part of the chart in question 8 and answer

question 9.

Choose values of your own for A until you have a good match for the plot. Record
your choices for A in the chart in question 8.
Repeat the activity, but this time choose the last (right-most) full bounce. Answer
questions 10, 11, and 12.
Repeat the data collection, but do not choose a single parabola. Record the time and height for each successive bounce. Determine the ratio between the heights for each successive bounce. Explain the significance, if any, of this ratio.
1. What physical property is represented along the x-axis? _____________________________________ What are the units? ___________________________________________________________________ What physical property is represented along the y-axis? _____________________________________ What are the units? ___________________________________________________________________ 2. What does the highest point on the plot represent? ________________________________________ The lowest point? ____________________________________________________________________ 3. Why did the Ball Bounce App flip the plot? _______________________________________________ 4. Why does the plot look like the ball bounced across the floor? _______________________________
5. Record the maximum height and corresponding time for the first full bounce. __________________ 6. Did the graph for A = 1 match your plot of the data from the first complete bounce? ____________ 7. Why or why not? _____________________________________________________________________ 8. Complete the chart below. A 0 -1 How do the data plot and the Yn graph compare?
9. What does a positive value for A imply? __________________________________________________ What does a negative value for A imply? _________________________________________________ What does a zero value for A imply? _____________________________________________________ 10. Record the maximum height and corresponding time for the last full bounce. __________________ 11. Do you think A will be bigger or smaller for the last bounce? ________________________________ 12. How did A compare? __________________________________________________________________ What do you think A might represent? ___________________________________________________

Run the EasyData App. To set up the calculator for data collection:
a. b. Select Setup (press p) to open the Setup menu. Press 2 to select 2: Time Graph to open the Time Graph Settings screen. Select Edit (press q) to open the Sample Interval dialog window. Enter 0.1 to set the time between samples in seconds. Select Next (press q) to advance to the Number of Samples dialog window. Enter 30 to set the number of samples. Data collection will last for 3 seconds.
When the settings are correct, choose Start (press q) to begin sampling. When the clicking begins, release the ball immediately (dont push) and step back. When the clicking stops, the collected data is transferred to the calculator and a plot of
distance vs. time is displayed. Answer questions 2, 3, 4, and 5.
Examine what happens for differing inclines.
Predict what will happen if the incline increases. Answer question 6. Adjust the incline to 30. Repeat steps 2 through 6. Add this plot to the drawing in

question 6, labeled 30.

Repeat steps 2 through 6 for inclines of 45 and 60 and add to the drawing.

Answer question 7.

Adjust the time values so that x = 0 for the initial height (the time at which the ball was released. You can do this manually by subtracting the x value for the first point from all the points on your plot, or you can enter L1(1)"A:L1NA"L1.
Calculate the values for a, b, and c for the family of curves in the form y = ax2 + bx + c
at 0, 15, 30, 45, 60, 90.
What are the minimum and maximum values for a? Why? Write an expression describing the mathematical relationship between a and the angle

of inclination.

1. Which of these plots do you think best matches the Distance-Time plot of a ball rolling down a ramp?
2. What physical property is represented along the x-axis? _____________________________________ What are the units? ___________________________________________________________________ What physical property is represented along the y-axis? _____________________________________ What are the units? ___________________________________________________________________ 3. Sketch what the plot really looks like. Label the axis. Label the plot at the points when the ball was released and when it reached the end of the ramp.
4. What type of function does this plot, between the two points you identified, represent?__________ 5. Discuss your change in understanding between the graph you chose in question 1 and the curve you sketched in question 3. ____________________________________________________________ ____________________________________________________________________________________
6. Sketch what you think the plot will look like with a greater incline. (Label it prediction.)
7. Sketch and label the plots for 0 and 90:

Teacher information

How might your classes change with a CBR 2 sonic motion detector?
The CBR 2 motion detector is an easy-to-use system with features that help you integrate it into your lesson plans quickly and easily. The CBR 2 motion detector offers significant improvements over other data-collection methods you may have used in the past. This, in turn, may lead to a restructuring of how you use class time, as your students become more enthusiastic about using real-world data.
Youll find that your students feel a greater sense of ownership of the data because they actually participate in the data-collection process rather than using data from textbooks, periodicals, or statistical abstracts. This impresses upon them that the concepts you explore in class are connected to the real world and arent just abstract ideas. But it also means that each student will want to take his or her turn at collecting the data. Data collection with CBR 2 motion detector is considerably more effective than creating scenarios and manually taking measurements with a ruler and stopwatch. Since more sampling points give greater resolution and since a sonic motion detector is highly accurate, the shape of curves is more readily apparent. You will need less time for data collection and have more time for analysis and exploration. With CBR 2 motion detector students can explore the repeatability of observations and variations in what-if scenarios. Such questions as Is it the same parabola if we drop the ball from a greater height? and Is the parabola the same for the first bounce as the last bounce? become natural and valuable extensions. The power of visualization lets students quickly associate the plotted list data with the physical properties and mathematical functions the data describes.
Other changes occur once the data from real-world events is collected. CBR 2 motion detector lets your students explore underlying relationships both numerically and graphically.

Explore data graphically

Use automatically generated plots of distance, velocity, and acceleration with respect to time for explorations such as:
What is the physical significance of the y-intercept? the x-intercept? the slope? the maximum? the minimum? the derivatives? the integrals? How do we recognize the function (linear, parabolic, etc.) represented by the plot? How would we model the data with a representative function? What is the significance of the various coefficients in the function (e.g., AX2 + BX + C)?

Explore data numerically

Your students can employ statistical methods (mean, median, mode, standard deviation, etc.) appropriate for their level to explore the numeric data. When you exit the EasyData App, a prompt reminds you of the lists in which time (L1), distance (L2), velocity L3), and acceleration (L4) are stored.
CBR 2 motion detector plotsconnecting the physical world and mathematics
The plots created from the data collected by EasyData are a visual representation of the relationships between the physical and mathematical descriptions of motion. Students should be encouraged to recognize, analyze, and discuss the shape of the plot in both physical and mathematical terms. Additional dialog and discoveries are possible when functions are entered in the Y= editor and displayed with the data plots. Performing the same calculations as CBR 2 motion detector is an interesting classroom activity. 1. Collect sample data. Exit the EasyData App. 2. Use the sample times in L1 in conjunction with the distance data in L2 to calculate the velocity of the object at each sample time. Then compare the results to the velocity data in L3.
(L2n+1 + L2n)2 N (L2n + L2n-1)2

L1n+1 N L1n

3. Use the velocity data in L3 (or the student-calculated values) in conjunction with the sample times in L1 to calculate the acceleration of the object at each sample time. Then compare the results to the acceleration data in L4.
A Distance-Time plot represents the approximate position of an object (distance from the CBR 2 motion detector) at each instant in time when a sample is collected. y-axis units are meters or feet; x-axis units are seconds. A Velocity-Time plot represents the approximate speed of an object (relative to, and in the direction of, the CBR 2 motion detector) at each sample time. y-axis units are meterssecond or feetsecond; x-axis units are seconds. An Acceleration-Time plot represents the approximate rate of change in speed of an object (relative to, and in the direction of, the CBR 2 motion detector) at each sample time. y-axis units are meterssecond 2 or feetsecond 2; x-axis units are seconds. The first derivative (instantaneous slope) at any point on the Distance-Time plot is the speed at that instant. The first derivative (instantaneous slope) at any point on the Velocity-Time plot is the acceleration at that instant. This is also the second derivative at any point on the Distance-Time plot. A definite integral (area between the plot and the x-axis between any two points) on the Velocity-Time plot equals the displacement (net distance traveled) by the object during that time interval. Speed and velocity are often used interchangeably. They are different, though related, properties. Speed is a scalar quantity; it has magnitude but no specified direction, as in 6 feet per second. Velocity is a vector quantity; it has a specified direction as well as magnitude, as in 6 feet per second due North.

Activity TEACHER INFORMATION
Velocity Test: Interpreting Velocity Graphs
1. There are currently four Motion Detectors that can be used for this lab activity. Listed below is the best method for connecting your type of Motion Detector. Optional methods are also included: Vernier Motion Detector: Connect the Vernier Motion Detector to a CBL 2 or LabPro using the Motion Detector Cable included with this sensor. The CBL 2 or LabPro connects to the calculator using the black unit-to-unit link cable that was included with the CBL 2 or LabPro. CBR: Connect the CBR directly to the graphing calculators I/O port using the extended length I/O cable that comes with the CBR. Optionally, the CBR can connect to a CBL 2 or LabPro using a Motion Detector Cable. This cable is not included with the CBR, but can be purchased from Vernier Software & Technology (order code: MDC-BTD). CBR 2: The CBR 2 includes two cables: an extended length I/O cable and a Calculator USB cable. The I/O cable connects the CBR 2 to the I/O port on any TI graphing calculator. The Calculator USB cable is used to connect the CBR 2 to the USB port located at the top right corner of any TI-84 Plus calculator. Optionally, the CBR 2 can connect to a CBL 2 or LabPro using the Motion Detector Cable. This cable is not included with the CBR 2, but can be purchased from Vernier Software & Technology (order code: MDC-BTD).

MDC cable

I/O cable

USB cable

Go! Motion: This sensor does not include any cables to connect to a graphing calculator. The cable that is included with it is intended for connecting to a computers USB port. To connect a Go! Motion to a TI graphing calculator, select one of the options listed below: Option Ithe Go! Motion connects to a CBL 2 or LabPro using the Motion Detector Cable (order code: MDC-BTD) sold separately by Vernier Software & Technology. Option IIthe Go! Motion connects to the graphing calculators I/O port using an extended length I/O cable (order code: GM-CALC) sold separately by Vernier Software & Technology. Option IIIthe Go! Motion connects to the TI-84 Plus graphing calculators USB port using a Calculator USB cable (order code: GM-MINI) sold separately by Vernier Software & Technology. 2. When connecting a CBR 2 or Go! Motion to a TI-84 calculator using USB, the EasyData application automatically launches when the calculator is turned on and at the home screen.
Real-World Math Made Easy
2005 Texas Instruments Incorporated

13 - 1 T

Activity 13 3. Place the Motion Detector at waist-high level for the walker. The walker should not be closer than 0.5 meter to the detector when data collection begins. Clear the area of other materials such as desks or chairs. 4. The instructions ask the student to walk in a particular motion: Stand still, walk away from the detector for two seconds, and then back to the detector for two more seconds. The objective of this particular walk is to create a graph that is simple to analyze in terms of slopes of segments. A more general graph can be used, but the analysis will be more complicated. 5. In order to keep the distance graph simple, the walker must maintain a constant rate while walking directly away and toward the Motion Detector.

SAMPLE RESULTS

Typical distance vs. time graph
Velocity vs. time data for same run

DATA TABLE

t point 1 0s d 0.73 m slope point 2 1.00 s 0.74 m segment 1 slope point 3 2.80 s 1.50 m segment 2 slope point 4 5.00 s 0.64 m segment 3 0.39 m/s 0.42 m/s 0.01 m/s

ANSWERS TO QUESTIONS

1. Using the distance graph, the velocity is positive from 1.00 to 2.90 s, as judged by the positive slope. 2. The slope is negative from 2.90 to 5.00 s, so the velocity is negative in this region.

13 - 2 T

What Goes Up? 3. The first 1.00 s has a velocity near zero, since the graph is nearly horizontal. 4. Sketches will vary; you can compare them to the original distance graphs. 5. Since the y-axis has units of meters, and the x-axis has units of seconds, the slope must have units of meters per second, or m/s. 6. Sketches will vary; you can compare to the original distance and velocity graphs. 7. The calculators graph is similar to my sketch, but is more irregular. 8. The calculator will have no way to choose landmark points for slope calculation (as I did) but must instead use many points. So, the calculators graph holds more detailed velocity information. 9. Actual Motion Person moves towards the detector Person stands still Person moves away from the detector 10. The walker started out standing just closer than 1.0 m from the detector, and was moving toward the detector when data collection began. The walker continued to move toward the detector for 2.0 s, at which time he or she turned around and walked away from the detector for two seconds. The speed away from the detector was a bit smaller than the speed toward the detector. Starting at t = 4.0 s, the walker stood still for the remaining time. Velocity Graph Characteristic negative slope zero slope positive slope