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AP Physics 1: Lab Report #1 – Velocity and Acceleration of a Toy Car Introduction In this lab investigation, our groups were given the instruction of finding the velocity, acceleration, and position of a moving toy car over a specified period of time. To conduct this investigation, the groups were each given a toy car, a spark timer, and spark tape. The spark-timer tool creates dots on the spark-tape for every tenth of a second, which we collected data from, and then used to answer questions pertaining to acceleration and velocity. Materials – – – – –

Spark-tape Spark-timer Toy Car Flat Surface Tools to record data, and plot on graphs

Background This lab consisted of using a couple of the most basic, yet vital formulas involved in physics: 1.) Velocity = Change in Distance / Time Taken 2.) Acceleration = Change in Velocity/ Time Taken Using these two formulas, physicists can determine numerous things about a given object— whether or not the object maintains a constant velocity, whether the object is speeding up or slowing down, whether heavier objects accelerate faster than lighter objects, and other things of that nature. In our situation, we collected our data and represented it in our graphs by using these distinct formulas, and were able to make conclusions about the way in which these toy cars traveled. Procedure To begin, each group member was given their own piece of spark-tape, which they fed through the spark timer, and taped to the end of the car. Then, simultaneously, the group member would turn on the car and the timer at the same moment and the car would take off. Our group then repeated that procedure with each of the pieces of spark-tape, and then went back to our desks to plot our data. We decided that we would need three separate values of distance to be able to create our graphs, so we began by measuring the distance between each dot in millimeters, and plotted them in accordance to the time that had elapsed (the distance between each dot represented a tenth of a second). The total

distance traveled of my toy car was 49.2 centimeters over 1.7 seconds, which I plotted in my first graph, labeled position. Next, we needed to graph velocity, so we remeasured the dots, but this time not compounding the distances between each of the dots, because the formula for velocity is measured as the change in distance over the change in time. Therefore, we calculated the distance between each individual dot, and then graphed it accordingly in the graph labeled “Velocity,” with my furthest distance being 33mm in a tenth of a second, and my shortest distance being 20mm in a tenth of a second. For the final graph, acceleration, our group then calculated the change of velocity over the change of time (the formula for acceleration), and then graphed it accordingly. Looking at my graph, you'll be able to notice that my lowest acceleration was zero meters per second squared, and my highest was five meters per second squared. Data Collected Position Compounded Distance (cm)

Time elapsed (seconds)

2 cm

.1 s

4 cm

.2 s

6.5 cm

.3 s

9.4 cm

.4 s

12.3 cm

.5 s

15.3 cm

.6 s

18.3 cm

.7 s

21.3 cm

.8 s

24.3 cm

.9 s

27.3 cm

1s

30.3 cm

1.1 s

33.3 cm

1.2 s

36.3 cm

1.3 s

37.5 cm

1.4 s

42.7 cm

1.5 s

45.9 cm

1.6 s

49.2 cm

1.7 s

Velocity Distance (mm)

Time Elapsed (seconds)

20 mm

.1 s

20 mm

.2 s

25 mm

.3 s

29 mm

.4 s

29 mm

.5 s

30 mm

.6 s

30 mm

.7 s

30 mm

.8 s

30 mm

.9 s

30 mm

1s

30 mm

1.1 s

30 mm

1.2 s

30 mm

1.3 s

32 mm

1.4 s

32 mm

1.5 s

32 mm

1.6 s

33 mm

1.7 s

Acceleration

Change in Velocity (m/s)

Time Elapsed (seconds)

0 m/s

.1 s

0 m/s

.2 s

5 m/s

.3 s

4 m/s

.4 s

0 m/s

.5 s

1 m/s

.6 s

0 m/s

.7 s

0 m/s

.8 s

0 m/s

.9 s

0 m/s

1s

0 m/s

1.1 s

0 m/s

1.2 s

0 m/s

1.3 s

2 m/s

1.4 s

0 m/s

1.5 s

0 m/s

1.6 s

1 m/s

1.7 s

Data Analysis/Conclusion 1.) The trend-lines, along with my hand-written graphs are connected to this report. Linear regression was used to calculate the slopes of the trend-lines. a.) Position: 3.36 x 10^-2 cm/s Velocity: 1.087 x 10^-1 mm/s Acceleration: -9.44 x 10^-2 m/s squared b.) Seeing as the data is fairly linear, this means that the car is moving at a constant rate of motion. If the data was all over the place, this would signify that the car's velocity is constantly fluctuating, thus resulting in data that looks scattered, as opposed to linear. 2.) Apart from acceleration, over time my velocity and position move at a fairly consistent upward trend over time. However, acceleration fluctuates from zero to five meters per second squared throughout the time trial. 3.) Position: a.) Person 1: 0.0336 b.) Person 2: 0.0442 This is a decrease of 0.0106 or a decrease of 23.98% Velocity: a.) Person 1: 0.1087 b.) Person 2: 0.2043 This is a decrease of 0.0956 or a decrease of 46.79% Acceleration: a.) Person 1: -0.0944 b.) Person 2: -0.0621 This is a decrease of 0.0323 or a decrease of -52.01% 4.) My numbers are different from my group members because there were probably discrepancies in the data when it came to particular measurements, and things of that nature. If we all were very precise with our measurements, then the numbers would have probably been significantly closer. 5.) Possible errors in the data could come from people not measuring correctly, obstructions when doing the trial runs of the toy car, and things like that. Also, our spark-tapes were not

all the same length, which could've possibly skewed our data, as some of our cars went for 1.7 total seconds, while others went for around 2.5 to 2.6. In order for us to ensure that we obtain more accurate data, our group would have to make sure to do everything in a uniform manner—same length spark timer, same method of measurement, same calculations, and same intervals on the x and y axes of the graphs. 6.) If a 20g mass was placed on top of the car, I would expect for the car to accelerate at a much slower rate, and also for the velocity to increase at a much slower rate. In other words, the car would not travel nearly as far in a short period of time, as it would without the 20g weight attached to it.

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Spark-tape Spark-timer Toy Car Flat Surface Tools to record data, and plot on graphs

Background This lab consisted of using a couple of the most basic, yet vital formulas involved in physics: 1.) Velocity = Change in Distance / Time Taken 2.) Acceleration = Change in Velocity/ Time Taken Using these two formulas, physicists can determine numerous things about a given object— whether or not the object maintains a constant velocity, whether the object is speeding up or slowing down, whether heavier objects accelerate faster than lighter objects, and other things of that nature. In our situation, we collected our data and represented it in our graphs by using these distinct formulas, and were able to make conclusions about the way in which these toy cars traveled. Procedure To begin, each group member was given their own piece of spark-tape, which they fed through the spark timer, and taped to the end of the car. Then, simultaneously, the group member would turn on the car and the timer at the same moment and the car would take off. Our group then repeated that procedure with each of the pieces of spark-tape, and then went back to our desks to plot our data. We decided that we would need three separate values of distance to be able to create our graphs, so we began by measuring the distance between each dot in millimeters, and plotted them in accordance to the time that had elapsed (the distance between each dot represented a tenth of a second). The total

distance traveled of my toy car was 49.2 centimeters over 1.7 seconds, which I plotted in my first graph, labeled position. Next, we needed to graph velocity, so we remeasured the dots, but this time not compounding the distances between each of the dots, because the formula for velocity is measured as the change in distance over the change in time. Therefore, we calculated the distance between each individual dot, and then graphed it accordingly in the graph labeled “Velocity,” with my furthest distance being 33mm in a tenth of a second, and my shortest distance being 20mm in a tenth of a second. For the final graph, acceleration, our group then calculated the change of velocity over the change of time (the formula for acceleration), and then graphed it accordingly. Looking at my graph, you'll be able to notice that my lowest acceleration was zero meters per second squared, and my highest was five meters per second squared. Data Collected Position Compounded Distance (cm)

Time elapsed (seconds)

2 cm

.1 s

4 cm

.2 s

6.5 cm

.3 s

9.4 cm

.4 s

12.3 cm

.5 s

15.3 cm

.6 s

18.3 cm

.7 s

21.3 cm

.8 s

24.3 cm

.9 s

27.3 cm

1s

30.3 cm

1.1 s

33.3 cm

1.2 s

36.3 cm

1.3 s

37.5 cm

1.4 s

42.7 cm

1.5 s

45.9 cm

1.6 s

49.2 cm

1.7 s

Velocity Distance (mm)

Time Elapsed (seconds)

20 mm

.1 s

20 mm

.2 s

25 mm

.3 s

29 mm

.4 s

29 mm

.5 s

30 mm

.6 s

30 mm

.7 s

30 mm

.8 s

30 mm

.9 s

30 mm

1s

30 mm

1.1 s

30 mm

1.2 s

30 mm

1.3 s

32 mm

1.4 s

32 mm

1.5 s

32 mm

1.6 s

33 mm

1.7 s

Acceleration

Change in Velocity (m/s)

Time Elapsed (seconds)

0 m/s

.1 s

0 m/s

.2 s

5 m/s

.3 s

4 m/s

.4 s

0 m/s

.5 s

1 m/s

.6 s

0 m/s

.7 s

0 m/s

.8 s

0 m/s

.9 s

0 m/s

1s

0 m/s

1.1 s

0 m/s

1.2 s

0 m/s

1.3 s

2 m/s

1.4 s

0 m/s

1.5 s

0 m/s

1.6 s

1 m/s

1.7 s

Data Analysis/Conclusion 1.) The trend-lines, along with my hand-written graphs are connected to this report. Linear regression was used to calculate the slopes of the trend-lines. a.) Position: 3.36 x 10^-2 cm/s Velocity: 1.087 x 10^-1 mm/s Acceleration: -9.44 x 10^-2 m/s squared b.) Seeing as the data is fairly linear, this means that the car is moving at a constant rate of motion. If the data was all over the place, this would signify that the car's velocity is constantly fluctuating, thus resulting in data that looks scattered, as opposed to linear. 2.) Apart from acceleration, over time my velocity and position move at a fairly consistent upward trend over time. However, acceleration fluctuates from zero to five meters per second squared throughout the time trial. 3.) Position: a.) Person 1: 0.0336 b.) Person 2: 0.0442 This is a decrease of 0.0106 or a decrease of 23.98% Velocity: a.) Person 1: 0.1087 b.) Person 2: 0.2043 This is a decrease of 0.0956 or a decrease of 46.79% Acceleration: a.) Person 1: -0.0944 b.) Person 2: -0.0621 This is a decrease of 0.0323 or a decrease of -52.01% 4.) My numbers are different from my group members because there were probably discrepancies in the data when it came to particular measurements, and things of that nature. If we all were very precise with our measurements, then the numbers would have probably been significantly closer. 5.) Possible errors in the data could come from people not measuring correctly, obstructions when doing the trial runs of the toy car, and things like that. Also, our spark-tapes were not

all the same length, which could've possibly skewed our data, as some of our cars went for 1.7 total seconds, while others went for around 2.5 to 2.6. In order for us to ensure that we obtain more accurate data, our group would have to make sure to do everything in a uniform manner—same length spark timer, same method of measurement, same calculations, and same intervals on the x and y axes of the graphs. 6.) If a 20g mass was placed on top of the car, I would expect for the car to accelerate at a much slower rate, and also for the velocity to increase at a much slower rate. In other words, the car would not travel nearly as far in a short period of time, as it would without the 20g weight attached to it.

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