Question

You're walking a dog through the park. There is a walking path from the entrance of the park to the exit that is 1 mile long and it is a straight line. While you're walking, the dog sees a squirrel which takes him off the path and around several trees until he gives up and rejoins you at the exit of the park. In total, he traveled 1.5 miles.

Answer 1

The question is about understanding the difference between distance and displacement. It requires recognizing that while the dog traveled a longer path, its displacement is just the straight line from start to end.

Step-by-step explanation:

The question revolves around the concept of distance and displacement. When you walk a dog through a park on a path and the dog runs off chasing a squirrel, the total distance the dog travels is not the same as its displacement. The dog traveled a distance of 1.5 miles, but its displacement – the shortest straight line between the starting point and the ending point – is only 1 mile, as the path from the entrance to the exit of the park is a straight line.

In the example of your friend's dog using a whistle to find her, the path the dog takes to her current location would incur an actual distance traveled but the displacement would be the direct line from where the dog started to where it found your friend. Displacement takes into account the final position relative to the initial position and does not account for the actual path traveled.

Understanding the distinction between distance and displacement is key. Distance measures the total length of the route taken by an object, disregarding its direction or changes in direction. Displacement, on the other hand, is a vector quantity that accounts for the overall change in position, giving the shortest distance from the start to the finish in a straight line, with direction accounted for.