Average velocity is calculated by taking the total distance traveled divided by the total time taken, while final velocity is the speed of an object at a specific moment, often influenced by acceleration. For example, if you drive 500 miles in 9 hours, your average speed would be approximately 55.56 mph. In contrast, if you speed up to 60 mph just before finishing a race, that is your final speed. In cases of constant acceleration, the average speed can be found by averaging the initial and final speeds. Understanding these concepts is crucial for physics applications, such as calculating the motion of falling objects.