Question

which statement is true regarding the relationship between distance and displacement?
a distance and displacement are always equal.
b distance is always different than displacement.
c distance is always less than or equal to displacement.
d distance is always greater than or equal to displacement.

Explanation:

• Option A: Distance (total path length) and displacement (straight - line from start to end) are equal only when motion is in a straight line without backtracking. So they aren't always equal.
• Option B: When an object moves in a straight line without changing direction, distance and displacement are equal. So distance is not always different from displacement.
• Option C: Displacement is the shortest path (straight - line) between two points. Distance is the total path traveled. So distance can't be less than displacement. It's the other way around.
• Option D: Distance is the total length of the path taken. Displacement is the straight - line distance between the initial and final positions. If the motion is along a straight line without any backtracking, distance equals displacement. If there is backtracking or non - straight - line motion, distance (total path) is greater than displacement (straight - line). So distance is always greater than or equal to displacement.

Answer:

D. Distance is always greater than or equal to displacement.