Group:
Faith Sutherlin


Jakob Wetmore

Jon King

Seth Johnston

  Lab: Interpreting and Matching
Displacement vs. Time Motion Graphs


 

Objectives:

  1. Create a Displacement vs. Time graph and match your graph with actual motion.
  2. Gain competence in the use of motion detector and related equipment.
  3. Understand the relationship between position vs. time, velocity and acceleration.
 

Materials:

TI-84 Calculator-Based Lab Unit (CBL-II)

Motion detector

Meter stick

Computer with LoggerPro software

 

Procedure:

Part I –

1.     Develop a position vs. time story that describes a body in motion incorporating at least the following four types of motion.

                  i.        standing still

                ii.        moving with constant velocity

               iii.        moving with variable negative velocity

               iv.        moving with variable positive velocity

2.        Illustrate the story on a position vs. time graph.  Use a legend to cross reference sections of the graph with the corresponding sections of the story.

3.        Underneath the graph, write instructions for moving in front of the motion detector according to the graph you have drawn.

Story

A) As Seth embarked on his journey to school from the church parking lot, he accelerated to 45 mph for 65 seconds.

B) He then slowed down gradually to 30 mph as he entered the school zone for another 30 seconds.

C) Then Seth stopped for 25 seconds.

D) He sped up to 15 mph as the traffic in front of Dean Rusk began to move for 5 seconds.

E) Seth suddenly slammed on his brake; he had hit Carly from behind at 5 mph, which caused him to stop again for 30 seconds.

F) Seth’s car would not start, so a group of firemen and policemen helped push his truck into the junior parking lot, which gradually accelerated to 20 mph for 25 seconds.

 G) It then rolled to a stop.



Picture

 

Directions for Moving
Keeping a binder or book in front of you, level with the motion detector, face the motion detector and move quickly at a constant speed for roughly one second, away from the machine. I reccomend taking about two steps. Then slow down for another two steps and stop for a short moment. Take a quick step, stop again. Take another quick step and stop again. I would attempt to outline the timeline for each motion in seconds, but that tended to be the challenge for my group. Repeat until it fits into the time frame--in our case, 5 seconds.


Part II – AT THE LAB STATION IN CLASS WITH A PARTNER


4. Measure out and mark meaningful locations on the floor and practice the motion needed to create the position vs. time graph.

 

5. Now it’s time for you to match your physical motion to your group’s descriptive motion graph. You have 3 attempts to match it as best you can. Save a copy best graph your motion creates and reproduce this graph using LoggerPro.

Seth's Wreck: Position vs. Time Graph

Picture
2m on graph = 2100m in story

5 sec. on graph= 180 sec. in story

Data from Logger-Pro Graph

The first column is time in seconds and the second column is position in meters.

0              0.105788

0.1          0.10551

0.2          0.141051

0.3          0.220461

0.4          0.298761

0.5          0.373728

0.6          0.436757

0.7          0.491733

0.8          0.540601

0.9          0.584193

1              0.624176

1.1          0.66638

1.2          0.706085

1.3          0.743292

1.4          0.778832

1.5          0.808264

1.6          0.834086

1.7          0.855466

1.8          0.872681

1.9          0.88462

2              0.89295

2.1          0.89878

2.2          0.900446

2.3          0.901835

2.4          0.904334

2.5          0.917106

2.6          0.938208

2.7          0.974304

2.8          1.02595

2.9          1.08259

3              1.12507

3.1          1.16006

3.2          1.1831

3.3          1.20087

3.4          1.21281

3.5          1.2217

3.6          1.22808

3.7          1.23114

3.8          1.23586

3.9          1.24502

4              1.26001

4.1          1.28695

4.2          1.32554

4.3          1.3758

4.4          1.43716

4.5          1.50713

4.6          1.57099

4.7          1.63846

4.8          1.83865

4.9          1.90085




Your lab report should include your story and corresponding graph, and the graph made using the motion detector.

Data Analysis:  Discuss differences between the descriptive graph and the graph generated by the motion detector.  What are the reasons for the differences?
   Generally speaking, the hand-drawn graph and the Logger Pro graph that was simulated using the motion detector are very similar. However, one difference is that the periods of time where the group was trying to create a velocity of zero are not as flat as in the hand-drawn graph. Because the range of motion that could be picked up by the motion dectector was limited, it was a challenge to keep the entire sequence of the story within 2 meters of actual distance and a small span of time. This may have caused the motion dectector to record the individual as having a very small velocity, while not quite recording zero. This could also be due to the fact that it is extremely difficult to have a human being stand perfectly still. Another difference is that the Logger Pro graph appears to have larger changes in position over smaller periods of time. This is because the span of time used to create the graph, 5 seconds, made for a challenging environment in which to simulate gradual changes in motion. This can be attributed to human error and an inability to estimate their own exact speed.
 

Conclusion:  Develop a conclusion that addresses the objectives of the lab.

 Because we drew the Position vs. Time graph first, we had a clear picture of what we were trying to recreate in real life. It was interesting to see how the motion of our bodies could mirror, at least to a slightly inaccurate degree, the motion of a car in a Position vs. Time graph. It allowed all of the group members to participate in brainstorming that served to create a more accurate graph by changing slight motion patterns. I gained a greater understanding of velocity in relation to Position vs. Time graphs. When the graph shows a concave up curve, the velocity is increasing; when the graph shows a concave down curve, the velocity is decreasing. When the graph shows a horizontal line, the velocity is zero. In all of these cases, whether the velocity at a certain moment is positive, negative, or zero can be determined by simply looking at the picture of the graph and observing the slope.This was helpful in determining the type of movements we should make to create the desired graph. Acceleration is described as changes in velocity, so if a Velocity vs. Time graph was created from the original graph, acceleration could be observed over the time period as well.