Which statement best describes the similarity and difference between $distance$ and $displacement$?

• A. $Distance$ and $displacement$ are both vector quantities that always have the same magnitude.
• B. $Distance$ measures the shortest path between two points, while $displacement$ measures the total path traveled.
• C. $Displacement$ is always greater than $distance$ for any motion.
• D. Both $distance$ and $displacement$ measure how far an object has moved, but $distance$ is a scalar quantity while $displacement$ is a vector quantity.

Answer: (D)

Verified step by step guidance

1. Understand the definitions: Distance is the total length of the path traveled by an object, regardless of direction, and is a scalar quantity (it has magnitude only). Displacement is the straight-line vector from the initial to the final position, having both magnitude and direction.
2. Recognize that distance measures how much ground an object has covered during its motion, while displacement measures the object's overall change in position.
3. Note that because distance is scalar, it cannot be negative and does not include direction, whereas displacement, being a vector, can be positive, negative, or zero depending on direction.
4. Understand that displacement can be equal to or less than the distance traveled, but never greater, because displacement is the shortest path between two points.
5. Conclude that the key similarity is both describe how far an object has moved, but the key difference is that distance is scalar and measures total path length, while displacement is vector and measures straight-line change in position.