A rate is defined as some quantity divided by a time interval. For walking, we would define the rate of walking (commonly called speed, if we just consider walking in one direction) as the ratio of the distance walked divided by the time interval taken to do the walking.

{\text{rate}} \equiv \frac{{{\text{distance traveled}}}}  {{{\text{time interval}}}}

From this definition you can also work backward. If you know the rate, or speed, of walking, as well as the time interval walked, you can find the distance traveled using

{\text{rate }} \times {\text{ time interval }} = {\text{ distance traveled}}

Strictly, the rate defined above is the average rate, so for non-constant speeds we will need to find the average speed for use with the formula.

A Motion Detector will give you the speed of a walker versus time. (The Motion Detector will actually give you velocity versus time, but for motion away from the detector speed and velocity are the same.) The product of rate and time interval is the area under the curve of the speed versus time graph.


  • Measure distance and velocity versus time information for a walker.
  • Compute the area under the velocity versus time graph, with units.
  • Compare that area to the distance traveled by the walker.