Models of Automobile Velocities

Data about velocity and position are pervasive in science. Recall that instantaneous velocity is the derivative of position as a function of time. Given data about the position of a moving object as a function of time, computing the object's velocity amounts to differentiating. Similarly, given information about velocity, one can compute position data by integrating.

Experiment #5

Conveniently, automobiles are equipped with instruments for measuring both velocity and position information. Recording mileage from the odometer gives position data, while the speedometer shows instantaneous velocity.

The idea of this experiment is to compute position data by numerically integrating some velocity data. Since we can use the odometer to determine the true distance travelled, in this special case, we can actually determine which kind of model function works the best for a specific data set. In this way, we can check some of our theoretical conclusions from the previous section.

Collecting Your Own Data

In groups of three or four people, arrange a time to go driving. Before you go, lay out out a course. The choice of course is up to you. But it should be fixed before you begin to record data. If possible, you should traverse the course once before recording data, in case of unforeseen problems.

Each group must have a designated driver. THIS PERSON DOES NOTHING BUT DRIVE. The driver is in complete control of the experiment, and must abort it at any time traffic safety requires a change of plan.

One person in the car is responsible for calling out speedometer readings at intervals agreed upon by the group in advance. This person also is reponsible for recording the odometer reading at the start and finish of the course.

The remaining person(s) in the car will record the time and velocity data according to methods agreed upon in advance by the group. Some suggestions:

  1. Collect data once a minute.
  2. Collect data every time you pass through an intersection or beneath a traffic light.
  3. Collect data at every stop sign.
  4. Collect data at random times.
Your data collection methods and course layout should generate about 20 data points. Collect data using two data collection methods. Traverse the course as many times as necessary to do this.
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The Geometry Center Calculus Development Team

A portion of this lab is based on a problem appearing in the Harvard Consortium Calculus book, Hughes-Hallet, et al, 1994, p. 174

Last modified: Fri Jan 5 09:51:02 1996