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.
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
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.
- Collect data once a minute.
- Collect data every time you pass through an intersection or beneath a
- Collect data at every stop sign.
- Collect data at random times.
Next:Integrating Experimental Data
Previous:Analyzing Accuracy of
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