# PHYS 2125 Graph Matching

PHYS 2125

Lab 2: Graph Matching

Objective:

The objective of this lab was to understand how graphs of position and time correlate to actual movement.

Equipment:

We used a motion sensor, rod base, rod, storage box lid, PASPORT Interface, and PASCO Capstone.

Theory and Equations Used:

We used the fact that the derivative of position is velocity and the derivative of velocity is acceleration. This knowledge helped us to match our movements to the graph because the position graph made you move at a certain velocity which we did not need to calculate, but learned to estimate. The velocity graph made us understand the relationship to acceleration by making us move quicker or slower to match the graph. We also used the equation: speed= (final distance-initial distance)/(final time-initial time) in order to calculate speed of the object on a velocity versus time graph.

Summary of Procedures

• We used the Rod Base and the Rod to fasten the Motion Sensor to the table;
• We connected the Motion Sensor to the Interface;
• We aimed the Motion Sensor at midsection of the body when standing in front of the sensor while holding the storage box lid in front of us to improve  the results of the reflections;
• We positioned the computer monitor so we could see the screen while moving away from or towards the Motion Sensor;
• Using the PASCO Capstone, we tried to match the graphs given to us as many times as needed to get the best scores possible and we recorded the datas we received.

Data Sheets:

Position Plot #1:

 Run # Score 2 97.5 3 97.3 4 99.2 5 98.4 6 99.1 7 94.6 8 99.3 9 99.2

Position Plot #2:

 Run # Score 10 66.3 11 74.2 12 79.6 13 39.6 14 39.7 15 38.9 16 81.3 17 85.8

Position Plot #3:

 Run # Score 18 75.4 19 59.5 20 66.2 21 -30.7 22 81.1 23 72.2 24 67.3 25 69.5

Velocity Plot #1:

 Run # Score 33 62.1 34 -381 35 63.2 36 70.6 37 60.6 38 61.0 39 73.6 40 67.0

Velocity Plot #2:

 Run # Score 44 14.3 45 47.1 46 30.2 47 30.0 48 32.9 49 20.0 50 9.0 51 42.1

Velocity Plot #3:

 Run # Score 53 49.4 54 63.9 55 61.3 56 75.2 57 44.3 58 51.3 59 45.2 60 37.6

Velocity Plot #4:

 Run # Score 63 23.2 64 17.6 65 25.8 66 -10.1 67 36.3 68 44.2 69 37.9 70 21.5

Post Lab Questions:

Position Plots

1. What does a horizontal line mean?

A horizontal line on a position versus time graph means that the object is at rest and traveled zero distance.

1. What is the difference between the parts of the plot with positive slope and the parts with negative slope?

The parts of the plot with a positive slope means that the object has a positive velocity while the negative slope has a negative velocity.

1. On the Position 3 plot, what is happening between 5 and 10 seconds? On the position 3 plot, the slope is negative meaning the object is slowing down and having a negative velocity between 5 and 10 seconds.
2. What parts of the plot were easier to match? What parts of the plot were the hardest to match? Why?

It was easier to match the straight lines because you did not have to move. It was hardest to match when the velocity changed because it was a little hard to judge exactly how fast you were meant to move.

Velocity Plots

1. What does a horizontal line mean?

A horizontal line on a velocity versus time graph means that the object is moving at a constant velocity with zero acceleration.

1. What is the difference between the parts of the plot with positive slope and the parts with negative slope?

The positive slopes on a velocity versus time graph tells you that the object is accelerating positively while the parts with negative slope tells you that the object has a negative acceleration.

1. Consider the Velocity 2 plot. What is the difference between places where the slope is large and places where it is near zero?

When the slope is large, the velocity is changing at a faster rate. When the slope is near zero, the object’s velocity is changing but at a slower rate.

1. Consider the Velocity 2 plot. Where is the acceleration largest? What is the speed at that point?

The acceleration with the largest value is in between 0 seconds and 2.5 seconds because it has a positive slope meaning the acceleration is also positive. The speed at that point is 0.12 m/s.

Equation: speed= (final distance-initial distance)/(final time-initial time) speed= (0.3 m - 0 m)/(2.5 sec-0 sec)= 0.12 m/s

1. Which of the four Velocity plots could qualitatively describe the vertical speed of a ball thrown vertically upward?

Velocity Plot #3 because it has a fast upwards acceleration, the ball being thrown, and then a constant downwards acceleration, gravity slowing the ball down.

Observations: Matching the position plots was easier than matching the velocity plots because it is easier to estimate in your mind where the graph wants you to be as opposed to how fast the graph wants you to move and speed up or slow down. We also noticed that if you tilted the lid slightly, the sensor would read weird data and it would basically ruin your run by giving you a negative score.

Conclusions: The relationship between position, velocity, and acceleration is an important concept for one to master. This lab helped us do that by giving us experience with what graphs should look like in person. For the relationship between position and velocity, we had to move forwards and backwards to match the position on the graph, and we had to move at the correct velocity. For the relationship between velocity and acceleration, we had to move forwards or backwards at the correct velocity to understand positive and negative velocity, and we had to move at the correct acceleration to match the graph.

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