Final answer:
The relationship between distance and difference is that distance is the absolute value of the difference, highlighting distance as a scalar quantity, which is only magnitude, while displacement is a vector quantity, defined by both magnitude and direction.
Step-by-step explanation:
When discussing the concepts of distance and displacement, it's important to understand their definitions and relationships. Distance refers to the total length of the path traveled between two positions and is a scalar quantity, meaning it has only magnitude and no direction.
On the other hand, displacement is a vector quantity that denotes the shortest path between the starting and ending points and is defined by both magnitude and direction.
The relationship between distance and difference, according to the options provided, is that the distance is the absolute value of the difference. This means that distance is always a non-negative number that represents how far apart two points are, irrespective of the path taken and without any consideration of direction. This is in contrast to displacement, which considers the direction and can have positive or negative values based on the assigned coordinate system.
As an example, during a round trip from home to school and back home, the distance would be the sum of the lengths of both trips, while the displacement would be zero, as the start and end points are the same. This illustrates how distance can differ from displacement, emphasizing the lack of direction in distance measures.