Physics Lab 3 Report

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Physics Lab 3: Average and Instantaneous Velocity Zyon Gomez, Allen Jones 02/02/2023

Introduction In this lab, we are trying to exemplify and understand the motion of objects. Furthermore, we are measuring and testing the relationships between displacement, velocity, and acceleration. Displacement is basically the difference between an object’s starting position and final position. Velocity is the time rate of change of displacement. Acceleration is the rate of change of velocity per unit of time. Purpose The objective of the first part of this experiment is to determine the average and instantaneous velocities of the metal slider. In the second part of this experiment we will determine the average acceleration of the metal slider. In this setup, the acceleration will be held constant and therefore the average acceleration is the same as the instantaneous acceleration. Diagram

Data Trial Average Time (s) Time Interval(s) Displacement (m) Average Velocity(m/s) 1 1.5637 ± 0.045 1.5475, 1.5729, 1.5707 ± 0.045 .8 ±.1 0.51160709 5.12 x 10 -1 ± 0.01 2 1.4131 ± 0.045 1.3872, 1.4227, 1.4293 ± 0.045 .7 ±.1 0.495364801 4.95 x 10 -1 ± 0.01 3 1.2469 ± 0.045 1.2359, 1.2524, 1.2524 ± 0.045 .6 ±.1 0.48119336 4.8 x 10 -1 ± 0.1 4 1.0807 ± 0.045 1.0674, 1.0905, 1.0841 ± 0.045 .5 ±.1 0.462663089 4.627 x 10 -1 ± 0.001 5 0.9077 ± 0.045 0.8921, 0.9123, 0.9188 ± 0.045 .4 ±.1 0.440674232 4.41 x 10 -1 ± 0.01 6 0.7157 ± 0.045 0.7091, 0.7158, 0.7222 ± 0.045 .3 ±.1 0.419170043 4.19 x 10 -1 ± 0.0001 7 0.5135 ± 0.045 0.5139, 0.5134, 0.5133 ± 0.045 .2 ±.1 0.389483934 3.9 x 10 -1 ± 0.1

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Graph 1 Slope = -0.986 Data Trial Average Time Time Intervals Displacement Average Velocity(m/s) 1 3.6455 ± 0.045 3.5617, 3.7596, 3.6151 ± 0.045 1.8 ±.1 0.493759429434 4.9 x 10 -1 ± 0.1 2 3.5532 ± 0.045 3.7535, 3.4939, 3.4123 ± 0.045 1.7 ±.1 0.478441967804 4.784 x 10 -1 ± 0.001 3 3.4057 ± 0.045 3.5501, 3.3338, 3.3332 ± 0.045 1.6 ±.1 0.469800628358 4.7 x 10 -1 ± 0.1 4 3.2612 ± 0.045 3.1973, 3.3851, 3.2012 ± 0.045 1.5 ±.1 0.45995339139 4.6 x 10 -1 ± 0.1 5 3.1380 ± 0.045 3.1565, 3.1408, 1.4 ±.1 0.44614404079 4.461 x 10 -1

3.1166 ± 0.045 ± 0.001 6 2.9731 ± 0.045 2.9607, 3.0059, 2.9527 ± 0.045 1.3 ±.1 0.4372540446 4.4 x 10 -1 ± 0.1 7 2.8083 ± 0.045 2.7980, 2.7642, 2.8626 ± 0.045 1.2 ±.1 0.427304775131 4.27 x 10 -1 ± 0.01 8 2.7718 ± 0.045 2.8445, 2.6644, 2.8066 ± 0.045 1.1 ±.1 0.396854029872 3.97 x 10 -1 ± 0.001 9 2.5218 ± 0.045 2.5526, 2.4127, 2.6001 ± 0.045 1.0 ±.1 0.396547499 3.965 x 10 -1 ± 0.001 10 2.3519 ± 0.045 2.4359, 2.2661, 2.3536 ± 0.045 0.9 ±.1 0.382669331179 3.83 x 10 -1 ± 0.01

Graph 2 Slope = -0.983 Sample Calculation

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Discussion and Error Analysis We found that the room for error of the gate timers was 0.0045 second as displayed in the data charts. This is a random error because the same thing being measured three times has three different measurements. This error affected our experimental values by making them vary slightly. The only other errors found within the experiment are ones calculated and/or given to us by the professor (0.1 cm uncertainty of the measurement tool). Conclusions This experiment helped us to exemplify the motion of objects by finding out the relationship of displacement, velocity, and acceleration. We also were able to find the constant acceleration of the glider interacting with all of the other variables in the room (gravity, velocity, etc.). We conclude that our acceleration was 0.966 m/s^2, our slope of the instantaneous velocity graph was -0.983.

Questions 1. Should the average velocity of the Lamborghini change or stay about the same as you decrease the time interval? The average velocity of the lamborghini should stay about the same as you decrease the time intervals in a perfect world. 2. What is the value of the y-intercept of your fit to the data points on the graph? What is the relationship between the y-intercept and the instantaneous velocity of the car as it moved through time t = 7.5 s? Our y-intercept was 5.12. 3. What are the sources of error in the calculation of the average velocity? Some sources of error in the calculation of the average velocity could be found when measuring the displacement and time intervals of the experiment. 4. The equation of motion of the Lamborghini is given by x(t) = 0.01t2, where x is the position in meters. This leads to a theoretical acceleration a=0.02m/s2. Is this number consistent with the acceleration from your measurement? Explain your answer. Our a = 0.966. Therefore, the number is not consistent. This is most likely because the two acceleration values are being taken from two different experiments.

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