Final answer:
Distance traveled equals magnitude of displacement only in straight-line motion without a change in direction. This happens because displacement considers the overall position change, and in a straight path without return, the distance covered and straight-line change in position are identical.
Step-by-step explanation:
Distance vs. Displacement
When considering the circumstances in which distance traveled is equal to the magnitude of displacement, we need to understand that this equivalence occurs only in a very specific scenario. Distance represents the total path length traveled by an object without regard to direction, while displacement is a vector quantity, meaning it has both magnitude and direction and represents the straight-line difference between the starting and ending points.
The only case in which the magnitude of displacement and distance traveled are exactly the same is during straight-line motion in one direction without any change in path. If, for instance, someone walks 5 meters east and stops, the distance they have walked is 5 meters, and their displacement is also 5 meters east, making the magnitude of displacement 5 meters as well. This scenario aligns with choice (d) from the provided options, illustrating that straight-line motion is the single case where these two measurements are equal. Any variation in path or a return journey would result in a difference between the two quantities as displacement takes into account the overall change in position, while distance traveled accounts for the entirety of the path taken.