CBL Unit Day #1

Introduction

Most students in our AP Calculus have had physics, but they have trouble understanding how distance, velocity and acceleration are related. This unit will help students explore these relationships as they are learning about the applications of derivatives and rates of change.

Equipment Required

• CBL unit
• TI-82, TI-83, or TI-85 graphics calculator with a unit-to-unit link cable
• Motion Detector.

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. Turn on the CBL unit and the calculator.

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

Experiment Procedure and Analysis

1. Select one student to "take a hike." Instruct he/she to walk at a constant rate. 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 assure that the rate is constant.

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. Make a chalk mark on the floor where the student's trip ended.

3. Have the class determine the rate at which the student walked. Use the TRACE command to find the coordinates of two data points and find the slope of the line between the two points. Ask students how the newly found information should be labeled. Remind them that this is a rate of change.

4. Select a second student to travel the same distance, using the chalk lines marked on the floor, 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.

Extend (student activities)

1. Analyze the graph. Where does the graph show that the rate was fastest, what is the slope in that area?

2. Where does the graph show that the rate was slowest, what is the slope in that area?

3. Explain how the slope of the tangent to the curve at a point is related to the velocity..

go on to DAY2!!!