Physics Lab 1- Graph Matching PDF

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LAB 1: Graph Matching

Maria M. Diaz Alonso 4157480 Florida International University PHY 2048L U24 Prof. Hugo Perez September 5, 2020

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PRELIMINARY QUESTIONS 1. Below are four position vs. time graphs labeled (i) through (iv). Identify which graph corresponds to each of the following situations and explain why you chose that graph. a. An object at rest Answer: Graph (ii) corresponds to an object at rest because the position is constant. As time changes, the position remains the same. Constant position indicates that an object is at rest. b. An object moving in the positive direction with a constant speed Answer: Graph (iv) corresponds to an object moving in a positive direction with a constant speed because it is positive and linear. As time changes, the position increases in a linear way which indicates a constant speed. The position increases at the same rate as the time. c. An object moving in the negative direction with a constant speed Answer: Graph (i) corresponds to an object moving in the negative direction with a constant speed because it is negative and linear. The position decreases in a linear way as time changes, which indicates a constant speed in a negative direction. The position decreases at the same rate of time. d. An object that is accelerating in the positive direction, starting from rest Answer: Graph (iii) corresponds to an object that is accelerating in a positive direction, starting from rest because it starts kind of flat, then increases, but, it is not linear. Since it is not a linear graph, then the speed is not constant. Also, it is moving in a positive direction because it is increasing. For an increment of time, the position x is moving higher and higher with each time increment.

2. Below are four velocity vs. time graphs labeled (i) through (iv). Identify which graph corresponds to each of the following situations. Explain why you chose that graph. a. An object at rest Answer: Graph (iii) corresponds to an object at rest. Since it is a velocity vs time graph, for an object to be at rest (stationary), the velocity has to be zero. This graph is the only one that has a constant velocity of zero throughout the whole-time interval.

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b. An object moving in the positive direction with a constant speed Answer: Graph (iv) corresponds to an object moving in a positive direction with a constant speed because it is a horizontal straight line on the positive side of the graph. This means that the velocity remains the same (constant) as time changes and it is moving in a positive direction because the velocity is positive (it is above the x-axis). c. An object moving in the negative direction with a constant speed Answer: Graph (ii) corresponds to an object moving in the negative direction with a constant speed because it is a horizontal straight line on the negative side of the graph. This indicates that the velocity remains the same (constant) as time changes and it is moving in the negative direction because the velocity is negative (below the x-axis). d. An object that is accelerating in the positive direction, starting from rest Answer: Graph (i) corresponds to an object that is accelerating in a positive direction, starting from rest because it is linear, positive, and increasing gradually. The graph also starts at zero, which indicates that it starts from rest. Since the velocity is constantly changing and increasing, it means that it is accelerating in a positive direction.

PROCEDURE Part I Preliminary Experiments 5. Examine the graph. Sketch a prediction of what the position vs. time graph will look like if you walk faster. Check your prediction with the Motion Detector. Answer: The position vs time graph looks steep and the line gets steeper as you walk faster. The slope also increases with faster speed (becomes much greater). Examples below:

Before (slower)

After (faster)

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Part II Position vs. Time Graph Matching 11. **Answer the Analysis questions for Part II before proceeding to Part III.** ANALYSIS Part II Position vs. Time Graph Matching 1. Describe how Hugo walked for each of the graphs that we matched. Answer:

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**For this graph, Hugo started with his position at 1 meter and stayed stationary for about 1 second. Then, he walked away from the sensor, increasing his distance and stopping at around 2.5 meters from the sensor, holding his position for around 3 seconds. He then walked towards the sensor, decreasing his distance and stopping at around 1.75 meters and holding his position steady.

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** For this graph, Hugo started at a distance of 0.5 meters from the sensor and walked away from the meter until he reached a distance of around 2.1 meters. He held his position there for about 3 seconds, then he walked towards the sensor in a way such that his speed started slow and then started walking faster and faster until he reached a distance of about 0.33 meters from the sensor. Then, he stopped and held his position. 2. Explain the significance of the slope of a position vs. time graph. Include a discussion of positive and negative slope. Answer: The slopes changes with the velocity. The faster the velocity (positive), the faster the position changes. So, the faster the velocity and greater the distance, then the steeper (higher) the slope is. The opposite is also true. When the velocity is slower (negative), the slope is more gradual (lower). A positive slope means that the distance away from the sensor is increasing and a negative slope means that the distance away from the sensor is decreasing. The value could be positive, but the slope would be negative. 3. What type of motion is occurring when the slope of a position vs. time graph is zero? Answer: If the slope is zero, it means there is no motion. The object is at rest or stationary. 4. What type of motion is occurring when the slope of a position vs. time graph is constant? Answer: If the slope is constant, it means that the position changes at the same rate as time. In other words, the velocity is constant (moving at the same speed) throughout the time interval.

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5. What type of motion is occurring when the slope of a position vs. time graph is changing? Test your answer to this question using the Motion Detector. Answer: When the slope changes throughout the time interval, it means that the velocity is not constant (accelerated motion) so it fluctuates throughout the time interval along with the distance (increasing, decreasing) resulting in different slopes. Sample below:

**Is this graph, it can be observed how the position and velocity fluctuate changing the slope. It oscillates between acceleration and deceleration.

Part III Velocity vs. Time Graph Matching 6. Describe how Hugo walked for each of the graphs that we matched. Answer: 1

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** In this graph, Hugo stayed stationary for about 2 seconds, then he started moving away from the sensor at 0.5 m/s (increasing distance/velocity from sensor) for about 3 seconds and stopped. He then started walking towards the sensor at 0.5 m/s (decreasing distance/velocity from sensor). 2

**For this graph, Hugo held his position steady for about 2 seconds. Then, he walked away from the sensor (increasing distance/velocity) at 0.9 m/s for about 1 second and stopped. He then started walking towards the sensor (decreasing distance/velocity) at 0.75 m/s for about 2 seconds and stopped. Then, he walked away from the sensor at around 0.33 m/s for about 1 second and stopped. He then started walking towards the sensor at around 1 m/s for around 2 seconds and stopped. 7. What type of motion is occurring when the slope of a velocity vs. time graph is zero? Answer: When the slope is zero, it means that the velocity is constant (same, does not change) throughout the time interval. The value of the velocity remains steady (constant velocity motion). 8. What type of motion is occurring when the slope of a velocity vs. time graph is not zero? Test your answer using the Motion Detector. Answer: If the slope is not zero, it means that it changes (positive or negative) throughout the time interval. This is a result of a changing velocity (not constant) that fluctuates (accelerates, decelerates) during the time interval. Sample below:

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