Ron, use you car as an example. The speedometer provides rate information, the odometer is a totalizer. Suppose your odometer is disabled and you need to calculate the mileage between two points. If you can maintain a constant speed for the entire duration of the trip, it's pretty simple; just multiply speed (Miles per hour) by time (Hours) to obtain the distance (Miles).
When you can't maintain a constant speed, it becomes a bit more difficult. If your car can accelerate from zero to sixty miles per hour in ten seconds, how much distance have you covered when you reach 60 MPH? If you answer 440 feet, you're assuming a constant acceleration rate.
Let's say you sample the speed once per second, and get the following data:
Start at 0 MPH
At 1 Sec. - 1 MPH You covered 1.5 Ft. in that second
At 2 Sec. - 3 MPH You covered 4.4 Ft. in that second
At 3 Sec. - 7 MPH You covered 10.3 Ft. in that second
At 4 Sec. - 15 MPH You covered 22.0 Ft. in that second
At 5 Sec. - 30 MPH You covered 44.0 Ft. in that second
At 6 Sec. - 45 MPH You covered 66.0 Ft. in that second
At 7 Sec. - 53 MPH You covered 77.7 Ft. in that second
At 8 Sec. - 57 MPH You covered 83.6 Ft. in that second
At 9 Sec. - 59 MPH You covered 86.5 Ft. in that second
At 10 Sec. - 60 MPH You covered 88.0 Ft. in that second
For a total of 484 feet. A different speed profile will result in a different distance travelled.
There is an inherent inaccuracy in the above procedure since you're not traveling at a constant speed over each time interval. By keeping the time increment short, you minimize the error. The calculated distance traveled is larger than the actual distance when you're accelerating; it's smaller than the actual when you're decelerating.
Hope this sheds some light on the issue.
ganutenator,
You'll minimize roundoff error if you accumulate the rate and divide the cumulative total by 86,400 instead of dividing the sample by 86,400.