Final answer:
The magnitude of the displacement vector cannot exceed the distance traveled because displacement is a vector quantity indicating the change in position with direction, while distance is the total path length without direction.
Step-by-step explanation:
The magnitude of the displacement vector cannot be more than the distance traveled. Displacement refers to the change in position from the starting point to the finishing point and is a vector quantity, which includes both magnitude and direction. On the other hand, distance is the total length of the path covered, irrespective of the direction, and is a scalar quantity. Therefore, it is possible for the distance traveled to be equal to or greater than the magnitude of the displacement, but not the other way around.
For instance, consider a professor pacing back and forth in a lecture hall: the professor may walk a total distance of 150 meters, but if they end just 2.0 meters to the right of their starting point, their displacement is 2.0 meters to the right, or simply +2.0 meters. The magnitude of displacement here is also 2.0 meters, while the distance traveled is much greater at 150 meters.
Displacement becomes equal to the distance traveled only when an object moves in a straight line in one direction without changing its path. For example, if you walk straight from point A to point B without turning or looping back, the distance you walked would be equal to your final displacement. Lastly, displacement is indeed a vector because it has both magnitude and direction, whereas distance, lacking direction, is a scalar.