# Trip Stories

Objective: The goal of this demo is to provide students with an opportunity to interpret graphical information from time vs. velocity graphs in order to create a story about an auto trip.

Level: Precalculus and calculus courses in high school or college.

Prerequisites: Familiarity with the concept of the slope of a line segment so that the velocity of an object can interpreted.

Platform:  Included is a set Excel worksheets that will work on both a PC and a MAC, together with an animation in both Flash and QuickTime.

Instructor's Notes: Understanding and working with information presented graphically is an important skill in a variety of areas. Here we present graphical information about an auto trip in the form of a time vs. velocity  graph. In most "trips" included in this demo the graph is piecewise linear so that the slope of a segment provides qualitative information about the velocity of the car during a particular interval of time. By describing the velocity of the auto on a segment a student can construct pieces of information about the trip to build a plausible story for the graph presented. To give an impression of the trip in the Excel worksheets the graph is generated by moving a slider that traces out the time vs. velocity graph. Three possible trip stories are presented. The user is asked to determine which of the stories best describes the auto trip represented by the graph. If the user feels that none of the supplied stories is appropriate, they can construct their own story to describe the trip.

Example 1. In Figure 1 we show a typical time vs. velocity graph for which a trip story can be computed.

 Figure 1.

Example 2. Next we provide a sample animation involving a time vs. velocity graph for a trip. We include descriptions of the segments of the trip that can help construct a story that corresponds to the auto trip represented by the graph.  This animation is available in Flash and QuickTime formats. In Figure 2 we display time vs. velocity graph used in the animation.

 Figure 2.

Click one of the following to view the sample animation.      Flash File          QuickTime File

We have developed six Excel files that contain time vs. velocity graphs for auto trips. To execute or download the individual files click on a picture below. Use the slider in the file to generate the time vs. velocity graph. Three possible trip stories are presented. Determine which of the stories best describes the auto trip represented by the graph. If you feel that none of the supplied stories is appropriate, construct your own story (on a piece of paper) to describe the trip.

Credits: This demo, the Excel files, and the animation were developed by

David R. Hill
Department of Mathematics
Temple University

and is included in Demos with Positive Impact with his permission.

1/30/2007           Last updated 1/30/2007     DRH