Analysis of the Integrated Velocity Data
Your position measurements are probably in miles or tenths of miles,
your velocity measurements are probably in miles/hour, and your time
measurements are probably in seconds or minutes. In order to make any
sense out of your numerical integration results, you will have to correct
for the fact that the data is not all recorded in the same units.
- What is the correction factor you must multiply by to convert
times in minutes to times in hours? What is the correction factor for
converting times in seconds to times in hours?
- Recall that if velocity is constant, then
distance = velocity x time. Assuming your
velocity measurements were in miles/hour, explain what factor you need
to multiply your own time measurements by to obtain distances in
- Consider the PC model for your velocity data. Explain the
physical meaning of the area under each flat segment of the graphs.
- Still thinking of the PC model for your data, explain why
multiplying the final result of your numerical integration by the time
conversion factor for your data will give the same result as first
converting all your data, and then numerically integrating.
- Use the above ideas to determine the approximation to the
total distance traveled given by each type of model function. Record
your answers, along with the actual distance travelled from your
odometer reading, in the table you were
given. Repeat for each of your three data sets. (You won't need to
recompute any numerical integrals, just multiply the answers by
an appropriate scale factor.)
Compare the results you obtained by numerical
integration with the actual odometer readings. Without necessarily
resorting to the careful methods of Question 11, write down the
absolute error for each method. (The absolute error is the difference
between your model's prediction and the true odometer reading.) Is
the method that was most accurate the one you would expect to be most
accurate in general? What about the least accurate method?
Previous:Integrating Experimental Data
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 14:29:11 1996