In this project, we explore distance in the context of metrics. Specifically, we take a look at an integral metric that is used to determine the distance between sets. The motivation of this project is to determine that the integral metric we use is meaningful in the context of our data set. The data set we explore consists of trajectories of cars along a portion of the highway. Through training, testing and evaluating this model on the data set, we can come to conclusions about the structure of the data and the success of this integral metric in terms of a classifier. In the end, we can determine whether or not this integral metric fits with the data set chosen and explore other areas where the metric could possibly succeed or where it might fail.