Walk This Way - Definition of Rate

Introduction

A rate is defined as some quantity divided by a time interval. For walking, we’d 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.

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

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

A Motion Detector will give you the speed of a walker vs. time. (The Motion Detector will actually give you velocity vs. 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 vs. time graph.

Objectives

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