Background: Velocity is a type of vector measurement that quantifies how far an object can move in a given time frame. Given that it is a vector, it is also direction dependent. Therefore, velocity is represented as an object's displacement over the change in time. Typically the units for this type of measurement are given as meters per second. There are two different ways to measure velocity. Average velocity is the total displacement over the total change in time for the period that is being examined. Instantaneous velocity is a measurement of the velocity at a single point in time. This is often represented as the derivative of the position versus time measurement. Both of these skills are very useful for physics and other academic studies as anytime there is a situation in which an object of interest is moving, it is likely necessary to understand how quickly that object is traveling and in what direction it is moving. In this experiment, the average velocity of a small battery-operated car was calculated by measuring the time it took for the car the travel 1 meter. Two different time measurement methods were attempted and the results were compared. 

Comparison of Methods: Overall, method 1 using the stopwatch timer on the cellphone was more conceptually straightforward and required less coordination between the partners than method 2 with the video recordings. Additionally, it was discovered the method 1 was a more accurate timing tool as it measured down to 0.01 seconds, while the video recordings only measured 1 second at a time. This meant that method 1 was the more reliable time measurement technique for its simplicity and accuracy. 

Equations:

Average velocity = displacement / change in time 

Average = sum of velocities / sample size

Standard Deviation = √(∑(x - u)^2) / n 

where x = an individual data point, u = the average, and n = the sample size

Grubb's Outlier Test = |outlier - average| / standard deviation

Discussion: While both techniques agreed that the average velocity of the battery-operated car was approximately 0.2 m/s, the results of this experiment suggested that method 1, the stopwatch timing function, was the more accurate time measurement tool. Method 1 allowed the average velocity (0.216 m/s) to be expressed with 3 significant figures as opposed to method 2 that only allowed the average velocity (0.2 m/s) to be expressed with 1 significant figure. This was because the stopwatch timer recorded up to 0.01 seconds while the video recordings only timed whole seconds. However, method 1 had a standard deviation of 0.030 which was approximately 14% of the the average velocity. There were a few measurements that initially appeared to be outliers (0.163 m/s and 0.170 m/s). When the Grubb's test was performed on each to determine if they were statistically able to be rejected from the larger data set, it was determined that neither measurement was a statistically large enough outlier to be rejected. Method 2 on the other hand had a standard deviation of 0.02 which was 10% of the average, almost exactly. The results suggested that method 2 was more precise than method 1 as the smaller standard deviation meant that the individual data points were closer to each other. This outcome was likely caused by the less specific measurements, allowing for more space for slight mistakes without impacting the data set. Regardless of the differences in the standard deviations though, method 1 was still determined to be the preferable method because it was more specific, easier to perform, and provided more accurate results than method 2.