# CBL Unit Day #1

#### This experiment was written to be used early in a first year calculus
course. It is designed to introduce students to the idea of velocity as
a rate of change.

##### created by Lari Garrison, Warren Township High
School 2/97

### 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.
- TI-GRAPH LINK (optional)

### 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.

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

### 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!!!