Final answer:
Despite Dugan swimming a total distance of 50 yards, his average velocity for the entire race is zero because the displacement is zero, as he finished at the starting point.
Step-by-step explanation:
To find Dugan's average velocity for the entire 50-yard freestyle race, we need to consider the total displacement and the total time taken. Since a 50-yard race involves going across a pool and back, the total displacement is zero (start and end points are the same). Therefore, despite Dugan swimming a total distance of 50 yards, his average velocity for the race is, by definition, zero because velocity is a vector quantity, which takes into account both magnitude and direction.
This scenario can be compared to the concept in physics that if an object returns to its original position, its displacement is zero, and thus its average velocity is zero as well. Despite the fact that Dugan covered a certain distance during the race, because he ended up back at the starting point, the displacement and hence the average velocity are zero.