# 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.

### Question 13

• 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 miles.

• 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.)

### Question 14

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?

Next:Conclusion
Previous:Integrating Experimental Data
Up:Introduction

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