Question

When is the magnitude of displacement equal to the distance?
A) When the motion is one particular direction
B) When the motion is in two directions
C) When the motion is in three directions
D) They are never equal

Answer 1

Hint: The displacement is the shortest straight line path between the initial and final positions. However, the distance covered by a body is the length of the actual path taken by a body while going from the initial to the final position.

Complete step by step answer:
The displacement covered by a body when going from an initial position to the final position is the length of the shortest straight line path joining the two points. However, the distance covered by the body will be the length of the actual path taken by the body when going from the initial to the final position.
When the motion of the body is only in one particular direction, then the path covered by the body to go from the initial and the final position has to be a straight line (since motion is only in one direction). Therefore, the magnitude of the displacement and the distance will be the same in this case since the displacement is the length of the straight line joining the two positions as explained above.
Hence, the correct option is A) When the motion is one particular direction.

Note: When the motion is in two or three directions, there is always a possibility that the body first covers a certain distance in one direction and then the rest in another direction, or even a third direction. The sum of all these lengths will always be greater than the length of the straight line path between the initial and final positions. Hence, options B) and C) are wrong.