Final answer:
The displacement for a 2.5-mile walk that starts and ends at the same location is zero, as displacement is the shortest distance between the start and end points and does not consider the actual path traveled.
Step-by-step explanation:
To find the total displacement of your walks every day, we need to consider the direction and magnitude of each segment of the walk. From your house, you go around the block, so you have a displacement of 0 miles in that segment. Then, you walk straight to the park, which is a displacement of 2.5 miles. Finally, you walk back to your house, which is another displacement of 2.5 miles. Since we are only considering the final displacement, we can add the displacements together: 0 miles + 2.5 miles + 2.5 miles = 5 miles
The question relates to the concept of displacement in physics, which is the shortest straight line distance between the initial and final position of an object. When you take your dog for a 2.5 mile walk around the block to the park and back, your route might involve a significant distance traveled, but if you start and end at the same location, your total displacement is zero. This is because displacement is a vector quantity that considers only the initial and final positions, rather than the path taken between them. For example, in the scenario given, no matter the distance walked, if you start at your house and return to it, your displacement is zero because there's no change in position.