CBL Unit Day #3

Students will do a quadratic regression to find a function that represents the distance a student walks with respect to time. Students will explore the velocity function and its relationship with the distance funciton by using the TI-82/83's numerical derivative function.

created by Lari Garrison, Warren Township High School 2/97
email lari@wtk.nslsilus.org

Equipment Required

Program Listing

This experiment requires that you download or enter the HIKER program into your TI-82, TI-83, or TI-85 calculator.

Equipment Setup Procedures

To connect the equipment:

1. Connect the CBL unit to the TI-82 calculator with the unit-to-unit link cable using the I/O ports located on the bottom edge of each unit. Press the cable ends in firmly.

2. Connect the motion detector to the CBL using the sonic port.

3. Connect the overhead calculator to the view screen, place the view screen on an overhead projector. Turn on overhead.

4. Secure the motion detector so that it is flat on a table top and perpendicular to the line of motion of the walker.

5. Turn on the CBL unit and the calculator.

The CBL is now ready to receive commands from the calculator.

Experiment Procedure and Analysis

1. Select a student to "walk a curve" that will resemble a parabola. He/she should start about 1.5 feet away from the motion detector. Have the student start before the motion detector is collecting the data to asure that the curve is as smooth as possible.

2. Run the program HIKER on the TI-82. It will instruct the user to "PRESS ENTER TO START GRAPH." When the CBL is collecting data a clicking noise will be heard. The TI-82 will graph the distance versus time as the student walks.

3. Do a regression on the data collected. Go to the STAT menu, then cursor over to CALC, then select QUADREG. (Instructions may vary from calculator to calculator).

4. Using a, b, and c just calculated, enter the new function in Y1. Turn off STAT PLOT, so the original graph is not graphed.

5. Ask the students what the velocity was as the student walked the curve. Have the students conjecture about what the graph of velocity versus time would look like.

6. To demonstrate what the velocity function looks like, in Y2 type in nDeriv(Y1, x, x). Graph the two functions on the same coordinate plane.

Extend (student activities)

1. Explain, using calculus, why the velocity function graphed above looks the way it does.

2. Suppose someone walked a curve that turned out to be a cubic, what would the graph of the derivative look like? Why?

3. Suppose the graph of the derivative was a sine curve, what would the graph of the distance function look like? Why?

4. Select a second student to walk the same path, but at at different rate. Follow steps 1-3 above again.

5. Have a third student walk the same distance in the same time, but at a rate which is not constant.

6. The class should analyze the graph. Where does the graph show that the rate was fastest, what is the slope in that area? Where does the graph show that the rate was slowest, what is the slope in that area?

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