Question
Physics 211 - This question and the one next week will deal with signs, notation, and terminology. (Analytical Geometry.)
The following diagram shows two points, P1 and P2, on an x-axis. The x-coordinates of the two points are denoted x1 and x2, respectively.
Definitions. Suppose an object moves from P1 to P2, then the displacement of the object is defined as the change in position, i.e., as the difference x2 - x1. This difference is also denoted Dx = x2 - x1 (read: "delta x"). This displacement must be distinguished from the distance travelled by the object, which is equal to the distance between the two points and which in turn is equal to the absolute value |x2 - x1|.
Note that a distance between two points and the distance travelled by an object can never be negative, but that a displacement can be negative.
Question. In the diagram above, the direction of the x-axis is to the right, i.e., the x-values are increasing as one goes to the right. (This is indicated by having the x-label of the axis on the right.) Suppose the points P1 to P2 remain unchanged, but that the direction of the x-axis is reversed. What are the signs of the displacement Dx = x2 - x1 and of the distance travelled by the object, |x2 - x1| then? I.e., indicate which ones, if any, of these quantities are positive and which ones are negative.
Answer
The diagram below shows an x-axis pointing to the left, opposite to that in the diagram above.
Now x1 > x2 so that x2 - x1 < 0. For example, if x1 = 10, then x2 = -4 so that x2 - x1 = -4 -10 = -14 < 0.
Thus, the displacement Dx = Dx is alwyas negative for this orientation of the x-axis. However, the distance travelled is still positive, by definition. In this specific example, it is equal to 14. (The SI-units, meters in this case, have been omitted here.)