Displacement

The first thing that we can quantify in our physics discussions is the change in the spatial (or position) coordinate. To do this, we will now define the terms displacement and distance. This is a classic example of the way words are used in science. These two words have definite mathematical definitions which you can not discern from their everyday usage.

Definition:

Displacement: final coordinate minus the initial. It has a direction (+ or -).

Definition:

Distance: absolute value of the displacement. Distance is always positive.

Here we use the notation that the present position is simply called x (without any subscript), and the initial position is called x₀ to remind us that this represents the value of x at time t = 0. With this, our definition for the displacement and for the distance is:

Displacement = $\Delta$x = x-x₀

Distance = |$\Delta$x| = |x-x₀|

Examples:

If I start at x₀ = 7.5 m and finish at x = 21.2 m,
then the displacement is $\Delta$x = 21.2 m - 7.5 m = 13.7 m, and the distance is |13.7| m = 13.7 m.
If I start at x₀ = 7.5 m and finish at x = -21.2 m, then the displacement is $\Delta$x = -21.2 m
-7.5 m = -28.7 m, and the distance is |-28.7| m = 28.7 m