TEACHER NOTES

Issues Related to the Problem

Make sure that you are free from liability before you set out to do this assignment.

This problem gets all of the students involved, is easy for everyone to do. It is a highly recommended problem for early in a course on differential calculus. Basically, the problem is for the students to go for a drive and record speed and distance data. Afterwards, of course, they are to study the data that they have collected.

Two other reasons I like this exercise:

This is an excellent opportunity for the students to submit early writing samples. The students don't mind, since they have a good understanding (or at least they think they do) of what they are writing about, and each group's paper is personalized.

This problem requires the use of groups. So, if you haven't found a nice group problem to get the class going, this is a good problem to try.

I purposely do not make this problem too hard. The goal is to give the students a (good) memorable example to carry with them through calculus. The harder problems build on this problem later in the course.

Prerequisites:

Students must be able to drive and have access to a car.

This project is designed to be done soon before the derivative is introduced.

Time Allotment - Time Management

Give part of a class period for the students to map out their game plan.

Provide about a week (including a weekend) for the students to gather their data.

Provide another week or so for students submit rough and final drafts.

Expectations

This is a simple problem that the students enjoy.

Future Payoffs

Extensions

The students can do differencing with their data to see how closely the numerical derivative of position fits the recorded speed data.

Further differencing allows students estimate the acceleration.

Graphing the curve smoothly offers a chance to talk about interpolation. If you are using Mathematica for example, you could discuss the mathematics involved in creating the interpolation function.

Here's some more suggestions offered by Brian Winkel.

How about integrating the velocity function to see how good it fits the position function?

Or differentiating the position function?

Or differentiating the velocity function to see the "G" forces they were subjected to?

References