TEACHER NOTES

ISSUES RELATED TO THE PROBLEM

While this problem entails curve fitting, we leave it up to the instructor to decide whether the students can use their computer software to perform curve fits or if they must derive the formulas for themselves.

Prerequisites

A knowledge of distance = rate * time, accumulation concept which leads to the integral. Interpretations of the definite integral.

Some experience with numerical integration.

Some experience with curve fitting (at least with computer software).

Time allotment - time management

Expectations

Future payoffs

Extensions

There are numerous ways to fit curves through the data: splines and polynomials of various orders are only starters. Ask students what shape they expect the power function to be, and have them fit a function of that shape. This will force them away from typical packaged curve fitting software. It will also give them the opportunity to familiarize themselves with how functions change shape as a function of their parameters.

References and Sources

Adair, Robert K.,"The Physics of Baseball", Physics Today, p. 26-31, May, 1995