Graphing Motion
Introduction

Motion is easy to recognize. We experience motion around us all the time. However, motion can be very hard to describe. One way to describe and better understand motion is through the use of graphs. A graph is a picture that show how two variables are related and is often easier to read than a data table. In the following activities, you will be collecting data using a motion detector and displaying that data in graphs. Your graphs will represent position as a function of time.


Using a Motion Detector
A motion detector works in the same manner that a flying bat navigates and detects its prey or submarines see each other and navigate the deep seas. Motion detectors emit sound that humans cannot hear. The pulses of sound reflect off objects and travel back to the motion detector, like an echo. Using this information, the whereabouts of the object the sound reflected from is determined and a point is plotted on the graph. This happens many times each second and a series of points get plotted to form a graph of position versus time.

Lets first predict what a graph of position versus time will look like for a person who originally stands 1 meter in front of the detector and walks away from the detector at a constant speed until he/she reaches a position 4 meters away from the motion detector.



Let's try it . . .

Let's start by standing in front of the motion detector. After selecting start the motion detector will begin to click (this lets you know it is collecting data).




Motion toward the detector
Suppose you stand 4 meters from the motion detector and for the first two seconds you do not move. Then, after two seconds you slowly walk toward the detector at a constant speed. On the graph below, sketch your prediction for the graph of position vs. time.




Motion toward the detector
Stand 4 meters from the motion detector. Start collecting data and remain still for the first two seconds. Then, walk slowly toward the detector with a constant speed. Stop when you are 1 meter in front of the detector.




Faster Motion toward the detector
On the graph below, sketch your prediction for motion that begins 4 meters away, remaining at rest for the first 2 seconds, and then walking toward the motion detector with a faster, constant speed than in the previous activity.




Faster motion toward the detector

Stand 4 meters away from the detector. Click "start" and wait 2 seconds. Then begin walking toward the detector with a greater speed than you walked in the trial before this one.






Matching the Motion
On the graph below, you will see a series of lines (let's call it the target graph). Your task is to match this target graph as best as possible by walking back and forth. Before you begin, view the graph and write down how you will walk to match this target graph.





After answering the question above, try to match this graph by collecting data using the motion detector as you walk back and forth.







View the target graph below. Describe how you will walk to match this graph. 0.0 -0.0 3.990025 2.984127 5.997506 3.0 6.9700747 1.5079365 8.004988 -0.0 9.975062 -0.0 Describe any differences between your prediction and the actual motion you performed to match the target graph.
Another graph match
Let's try one more match.















For the target graph below, describe how you will walk to match the target graph best. 0.0 3.015873 1.990232 0.984127 2.991453 0.984127 7.008547 3.984127 7.997558 1.5079365 9.97558 1.5238096 During which interval were you moving the fastest? 0 seconds - 2 seconds 2 seconds - 3 seconds 3 seconds - 7 seconds 7 seconds - 8 seconds 8 seconds - 10 seconds What evidence from the graph supports your answer to the previous question?
How fast were you moving?
You can determine the speed of the person who was moving by calculating the slope of the line. To find the slope of the line, m, you must determine the "rise" on the graph for a particular "run." The rise is a paricular change on the vertical scale for a certain change on the horizontal scale.

m = rise/run