Final answer:
The magnitude of a particle's displacement cannot be greater than the distance traveled, as displacement refers to the straight line distance between two points considering direction, while distance traveled is the total path length covered.
Step-by-step explanation:
The magnitude of a particle's displacement can never be greater than the distance traveled by the particle. Displacement is defined as the straight line distance between the starting and ending points, taking into account the direction, thus it is a vector quantity. The distance traveled is the total length of the path the particle took, regardless of its direction, making it a scalar quantity. Therefore, distance traveled can be equal to or greater than the magnitude of displacement, but not the other way around.
For instance, if you walk in a straight line from point A to point B, the magnitude of your displacement will be equal to the distance you have walked. However, if you take a more circuitous route to get from point A to point B, you will travel a greater distance, but your displacement, being the straight line from start to end, remains unchanged.
It is also important to note that displacement can be negative when the final position is less than the initial position, illustrating direction in a coordinate system. Average velocity can be negative as well when displacement is in the negative direction. Additionally, when motion is linear and in a single direction without any return, the displacement is exactly the same as the distance traveled.