Final answer:
The question inquires about calculating distance and displacement in physics, incorporating the understanding of vectors. Distance refers to the complete path taken, while displacement is the shortest path between two points with a specific direction. Methods such as vector addition and the Pythagorean theorem are used to find the resultant magnitude and direction of displacement.
Step-by-step explanation:
The question presented requires understanding of concepts in physics, specifically on the topic of displacement and distance traveled. When you're asked to calculate the distance between two points and the displacement from start to finish, you're dealing with vectors and their properties. Displacement is a vector quantity that has both magnitude and direction. It represents the shortest path between two points. On the other hand, the total distance traveled may include the entire path taken, regardless of the starting and ending points.
To calculate the total distance traveled (path A or path B) as outlined in the figures, you would sum up the lengths of each segment traveled. For the magnitude and direction of displacement, you would consider only the straight-line distance and direction from the start to the finish. For vector problems, such as walking 18.0 m west and 25.0 m north, you would use vector addition to find the resultant displacement vector R, by calculating the magnitude using the Pythagorean theorem (R = √(A^2 + B^2)) and the direction using trigonometry (tanφ = opposite/adjacent).