Avg vs. Inst Velocity Lab Report

Average vs. Instantaneous Velocity Hutton 2 Purpose: The purpose of this experiment is to compare and analyzed the relationship between instantaneous and average velocities. Instantaneous velocity is the velocity, or speed with direction, at exactly one particular moment in time, as if you were to take a snapshot and calculate the velocity of an object based on just that one instant. On the other hand, average velocity is calculated by the change in position over a certain period of time. In essence, average velocity can be seen as an entire set of measurements to get a velocity, while the instantaneous velocity can be seen as only one decreased measurement out of that set to get only that particular velocity in time. In order to measure average and instantaneous velocities in a demo, we used a glider passing between two photogates over a distance on an air track. For the first component of the lab, the runs were timed and based upon the fluctuating distances, the average velocities were able to be calculated. In the second portion of the experiment, instantaneous velocities were calculated based upon a series of runs and then those values were averaged to find one conclusive instantaneous velocity. Results: Average Velocity vs. Distance Data Time Between Gates (s) 5.00 4.64 4.22 3.82 3.41 3.02 2.68 2.29 1.90 1.59 1.31 0.94 0.64 0.34 Distance (m) 1.40 1.30 1.20 1.10 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 Average Velocity (m/s) 0.28 0.28 0.284 0.288 0.293 0.298 0.299 0.306 0.316 0.315 0.305 0.319 0.313 0.294 Calculations: Each of these 14 trials generated average velocities using the following equation: V avg = ∆x ∆t The ∆ x represents displacement, or the change in position, with respect to the change in time over a certain period. For example, the average velocity for our first trial was calculated as shown below and followed for each trial after: Hutton 2 Average vs. Instantaneous Velocity V avg = 1.40 mm =0.28 m/ s 5.00 s These values were then graphed in a distance versus average velocity graph to see the overall trend of how the fluctuating distance affected the velocity. The graph is shown below. Questions: 1. The lab procedures explained that the photogates needed to begin 140cm apart, which meant that the first photogate was located at 30cm and the second photogate was located at 170cm. This also fit well with the starting location of the glider, which was measured by lining up the very front of the glider with the 20cm mark. Our method for measuring the photogate positions was to use the centimeter marks on the air track itself. We lined up the poles of the photogates to the tick mark on the air track and positioned the sensor as straight over the track as possible. This may have allowed for some error due to the exact position of the photogates may be relative to the angle at which it is looked at. However, we used the tick marks on both sides of the air track with the flat edge of a rule to get the photogate as straight as possible. 2. According to the graph of our data shown above, the closer together the photogates were, the higher the velocity was. On the other hand, the further apart the photogates were, the lower the velocity. In essence, the general trend was that the velocity of the glider was higher when the photogates were closer. Therefore, this would indicate that distance and velocity are inversely proportionate. 3. The instantaneous velocity at the center of the track in part 2 was found by taking the derivative of the position with regard to the timing. At the center of the track, which was the last run from part 2, the two photogates were 0.10mm apart. Based off of this one reading, we could approximate the instantaneous velocity of this run to be 0.29m/s. 4. Our values fluctuated a bit, which was reflected in the graph, and that may be due to some unexplained error. There were several trials performed for each of the runs because we made the mistake of passing the glider back through the photogates between each of Average vs. Instantaneous Velocity Hutton 2 the runs and we did not add the 20g of weight to slant the air track. This could have caused a couple of the outlying fluctuations seen in our graph and the trend found in the data table. However, our estimated instantaneous velocity seemed to be fairly similar to those points found in part 2 of this experiment. The instantaneous velocity found in the third part of this experiment was 0.333 m/s with a measure of uncertainty of ±0.023. This does not exactly cover our entire spread of data for average velocity, but the numbers are still relatively close, but not exact. 5. This value is not an instantaneous velocity because the PASCO was flagging the precise moment and position of the glider and comparing it with other instantaneous velocities. The difference between actual instantaneous velocity and these readings is that instantaneous velocity is the result of a single reading from a single instance in time and position. For part 3, we had five different distances for the runs and after gathering all of the data for those five different runs, then the average of those was collected and presumed to be the instantaneous velocity of the data. Conclusions: This experiment was harder to complete successfully, as there were quite a few technicalities that would result in error if not completed correctly. As far as our experiment specifically, we attained extremely high velocities, but this was due to measuring the distances in centimeters rather than meters, which was a simple fix. Another error that occurred in during our lab was that the glider could not pass or be slid through the photogates between runs or else it would skew the data collection and cause it to be errored. However, despite these potential errors, this lab was a good demonstration of average velocity compared to instantaneous velocity. There were several errors previously mentioned that occurred during this lab experiment, but regardless of that, our estimated instantaneous velocity, which was 0.333 m/s ±0.023, was relatively close to our estimated instantaneous velocity from part 2, which was 0.29m/s. In conclusion, this was a great demonstration of both instantaneous and average velocity and it appears to be relatively accurate, as well.