Lab 3- group 8

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INSTANTANEOUS AND AVERAGE VELOCITY Lab 3. Instantaneous and Average Velocity and Speed Introduction: In this laboratory, software will be used to find speeds and they will also be compared. We will have to calculate the average speed to compare the values between 2 graphs. First of all, what is instantaneous and average velocity ? instantaneous speed is the speedometer of a moving car at a precise moment. At the moment it indicates your speed at that exact moment. We can say that the average speed looks like the general speed during the entire trip. It is the total distance you have traveled divided by the total time it took you to get there.

INSTANTANEOUS AND AVERAGE VELOCITY Lab Equipment - Blue cart ( Bluetooth ) - Classmates to share data - Pasco software - Dynamic track feet - A platform for the car Instantaneous Procedure:

INSTANTANEOUS AND AVERAGE VELOCITY 1. Use a Multi-Coordinates tool on the Velocity vs. Time graph to find the maximum positive instantaneous velocity near the beginning of the run. Then on the Speed vs. Time graph, find the instantaneous speed at this same time. Record the values. How do the two values compare? The maximum positive instantaneous velocity on the Velocity vs Time graph is (.594). The instantaneous speed on the Speed vs Time graph is (.59) . Both values are similar as the speed is exactly at .59 and the velocity is at .594 but when rounded to two decimal places it would display as .59 as well. 2. Near the middle of the run, find the instantaneous velocity and speed at the moment when the cart reached its highest point and reversed direction, and record. How do the two values compare? The instantaneous velocity is (-0.003) and the instantaneous speed is (0.00). The two values compared are similar rounded to two decimal places but the velocity is negative and the speed is at zero 3. Near the end of the run, find the maximum negative instantaneous velocity, and the instantaneous speed at this same time, and record. How do the two values compare? The maximum negative instantaneous velocity on the Velocity vs Time graph is (-0.523). The Instantaneous speed on the Speed vs Time graph is (0.52). The Values compared are the same but the Velocity is negative and the speed is positive. 4. What is the difference between speed and velocity? The speed and the velocity have similar values, but the velocity carries greater direction which results in negative values and the speed does not as it takes more on the total distance of time which would result more in positive values. Interval A

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INSTANTANEOUS AND AVERAGE VELOCITY 1. Use the Highlight tool on the Velocity vs. Time graph to highlight the data for Interval A: from the moment when the velocity was at its positive maximum, to the moment when the velocity was zero. Turn on the Statistics, and then turn on Mean. Record the mean velocity value. The Mean For Velocity was 0.304 2. Repeat for the Speed vs. Time graph, highlighting the same time interval, and recording the mean speed value. How does it compare to the mean velocity value? The Mean For Speed is .30, The mean for the velocity and speed are similar in their values rounded to two decimal places 3. On the Position vs. Time graph, add a Coordinates/Delta tool and use the Delta tool to find delta x and delta t, record these values. The Value of displacement for delta x is 0.4039 m(.5215-.1176), and the time interval for delta t is (2.225 - .850s) = 1.375 s 4. Calculate and record the average velocity for this interval using Equation 1: How does this compare to the mean velocity found on the Velocity vs. Time graph? 4309 / 1.375 = .313 m/s, 5. For motion where the cart moves in one direction only (like only up the track), the distance traveled is the absolute value of the displacement of delta x. The average speed is found in equation 2. Use Equation 2 to calculate the average speed for this interval. Record, and compare to the mean speed found on the Speed vs. Time graph. |.4309| / 1.375 =.313 m/s

INSTANTANEOUS AND AVERAGE VELOCITY Interval B:

INSTANTANEOUS AND AVERAGE VELOCITY 1. Use the Highlight tool on the Velocity vs. Time graph to highlight the data for Interval A: from the moment when the velocity was at its negative maximum, to the moment when the velocity was zero. Turn on the Statistics, and then turn on Mean. Record the mean velocity value. The mean negative maximum velocity is -0.269 equivalent (-0.270) 2. Repeat for the Speed vs. Time graph, highlighting the same time interval, and recording the mean speed value. How does it compare to the mean velocity value? The mean negative maximum speed is 0.27, Both negative means in velocity and speed are similar, but velocity mean is negative and speeds mean is positive . 3. On the Position vs. Time graph, add a Coordinates/Delta tool and use the Delta tool to find delta x and delta t, record these values. The delta t is (3.875-2.225) = 1.650, and delta x is (.0782 - 0.5215) = -0.4433 4. Calculate and record the average velocity for this interval using Equation 1: How does this compare to the mean velocity found on the Velocity vs. Time graph? -0.4433/1.650 = -0.269 5. For motion where the cart moves in one direction only (like only up the track), the distance traveled is the absolute value of the displacement of delta x. The average speed is found in equation 2. Use Equation 2 to calculate the average speed for this interval. Record, and compare to the mean speed found on the Speed vs. Time graph. |-0.4433| / 1.650 = 0.269

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INSTANTANEOUS AND AVERAGE VELOCITY Combined A and B Intervals: 7. On the Velocity vs. Time graph, highlight the data for the Combined Interval A & B: from the moment when the velocity was at its positive maximum, to the moment when the velocity was at its negative maximum. Record the mean velocity value. Mean velocity = -0.003 m/s 8. Repeat for the Speed vs. Time graph, highlighting the same time interval, and recording the mean speed value. How does it compare to the mean velocity value? For Intervals A and B separately, the mean speed was approximately equal to the mean velocity. But for Combined Interval A & B this is not true. The following calculations will help you understand why this is so. The Mean speed = 0.29 m/s They are not close to each other based of the majority distance from one another. 9. To find the average velocity for this interval, we modify Equation 1 to include the sum of delta x values, and the sum of delta t values from both intervals A and B. Calculate and record the average velocity for this interval using this modified Equation 1. How does this compare to the mean velocity found on the Velocity vs. Time graph? .4039 + -.4433 / 1.375 + 1.650 =- 1.3 x 10^-2 The values are not similar as it could be based off of an error of a digit or two when using the PASCO. 10. To calculate average speed for this Combined Interval A & B, remember that the cart changes direction at the top of the track. So the total distance traveled is the sum of the distances traveled for Interval A and Interval B. So we can modify Equation 2 like so, Notice that we need to take the absolute values before adding the terms in the numerator! Calculate the average speed with

INSTANTANEOUS AND AVERAGE VELOCITY the modified Equation 2. How does this value compare to the mean speed found from the Speed vs. Time graph? |.4039| + |-.4433| / 1.375 +1.650 =.280 The answer is almost identical to the one found in question 8, yet the values are only 1 digit off.

INSTANTANEOUS AND AVERAGE VELOCITY Conclusion Instantaneous velocity is represented by the velocity of an object at a precise moment, on the other hand, average velocity is total displacement divided by total time. Doing experiments to compare these concepts using graphs is important for several reasons, one can be comparing graphs of instantaneous and average speed, we can identify through observation how these concepts apply in various practical situations, such as car safety tests, launches of rockets and motion analysis in sports. Comparing graphs in experiments related to instantaneous and average speed is crucial for both theoretical validation and practical applications, allowing us to make informed decisions and advances in various domains.

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