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# Determine the Relationships Between the Position and Time Once a Buggy Shifts from Its Origin

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The purpose of this lab is to find the relationships between the position and time when a buggy moves away from the origin. This experiment was done to determine if time, measured in seconds, and the position from the origin, measured in meters, made a direct correlation. The data collected shows that, when the buggy was going in a straight, or somewhat closely straight when time goes by, the position from the origin also increases. The graph that was made from the collected data depicted a positive correlation when all the points been graphed into a scatter plot, with the Y—axis being the position from origin, and the x-axis being time the buggy started to move from the initial position from the origin. When adding the best fit line, the correlation was 09955, which meant the there was a strong correlation between the position from the origin and the time. In conclusion, when the buggy was moving constantly, the position is increased when time is increased Introduction.

The lab was performed to understand the relationship between the position from the origin and time that goes by, and to determine whether it has a direct relationship between them. From the pre-lab discussion, the class learned new variables that could be measured: speed, distance, mass, charge of the battery in the car, time, volume, and weight Distance and clock—reading, which was time, was variables that was used in this lab, because with the materials, it was the most easiest to measure. The distance was noted to be in meters (m) while the clock reading was in seconds. To establish the distance, there needs to be an origin in order pinpoint where the object is and how far away it is; this became known as the position, which is the point that is away from the origin. The variables for position is x, and t is for time, Using a buggy, meter sticks, a stopwatch, and some tape, the groups were able to find the positions and the time, by placing the buggy, which drove in a positive direction, on an origin and setting a time limit to stop the buggy and seeing the position away from the origin (run on sentence need fix).

The relationship between the position and time is needed to be defined because there is a possibility that an equation can come out of the connection, which can later help find missing positions at certain times. The group hypothesized that when the time increases> the position from the origin also increases proportionally, creating a direct positive relationship. This is because the buggy was shown to seemingly move at a constant rate, so therefore, the position of the buggy will continue to move away from its starting point as time goes on. Methods: In this experiment> time (t) is the independent variable, and position (x) is the dependent. To begin, gather all materials: 3 meter sticks, a motorized toy car, stopwatch, and tape. Then find a flat surface to perform the experiment on, such as a school hallway, Place a piece of tape to mark the initial position on the ground Make one person responsible for the stopwatch, and one person for the toy car. Place the toy car at the starting point (front tires behind the tape) and reset the stopwatch.

When the stopwatch starts, the car must simultaneously start by being turned on, At 1 second, stop the toy car and the stopwatch simultaneously. Repeat from when the buggy is at the starting point and stop at 2, 3, 4, 5, and 6 seconds Afterwards, perform the trial two more times, in total of three trials. Remember to record how many meters away from the original position the buggy was for each time the stopwatch was stopped. Results and Discussion: Nine groups did this experiment, All groups were required to make a scatter plot depicting their collected data. 9 out of 9 groups had scatter plots of position verses clock reading Based on the above evidence, we can conclude that there is a directly proportional relationship between the position of the buggy and the time of the stopwatch. Many groups had similar data, and got points that could be put into a linear regression (best fit line). The course of action was to generate the linear regression for the plots, and calculate the equation for the slope and y-intercepts.

The correlation for the best fit line is also found in this partwhen the best fit line was added, there was similarities amongst the group, It was concluded that the best fit line was the slope. The slope stood for the meters in position per second (m/s). So for each second, the buggy would move proportional amount of meters, 8 of the 9 groups have gotten a positive slope, while the 1 gotten a negative slope. It is established that the direction in which the front bumper of the buggy is facing is considered the positive position values. Because all the buggies had a different speed, there was no exact same slope, The Y-intercept stood for the position from the origin (x), which is in meters. Y-intercept is the initial distance from the origin, Out of 9 groups, 8 groups started at the origin, meaning their intercept was at zero. The other group had to start at 5 meters away from the origin, so their y-intercept was off. When doing the 5% rule, only 7 out of 9 groups have y-intercepts that are close to the origin and 2 out of 9 groups had an intercept that was negative, The 5% rule states to take the y-intercept and divide it by the maximum y-value.

Then times it by 100, and if its under 5, then the y-intercept does not need to be added into the equation. A correlation was found and 9 out of 9 groups had a correlation of 0.99 or higher. This meant that there is a stronger direct proportional relationship between the clock reading and the absolute value of the position. In conclusion, based on the data and the scatter plot, there is a relationship between time and position of a moving object. This relationship is later found out as the velocity. Because the buggy generally did not move in a straight line the whole time, it could not be counted as speed, due to the fact speed does not need direction as part of its equation. Velocity however does count direction as part of its equation, along with the distance and the time. The general equation is VZX/t, where V is velocity, X is position, and t is the seconds it took when the buggy was moving.

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