Negative and Positive Displacements

Example 2-1 Negative and Positive Displacements

Find the displacement of a cyclist who rides

a.
from a position of 500 m to a position of 300 m.

b.
from a position of −500 m to a position of −300 m.

c.
Find the distance traveled by the cyclist in each case (assuming no backtracking).

Solution

Sketch the situation. It is important to have a clear picture of what is happening. Figure 2-5 shows the displacements asked for in a and b.

Figure 2-5 Positions and displacements for Example 2-1.

Use the definition. Displacement is defined as Δx = x₂ − x₁, where x₁ is the earlier and x₂ the later position. In a, x₁ = 500 m and x₂ = 300 m, so

and is negative. In b, however, x₁ = −500 m and x₂ = −300 m, so

and is positive.

c.   The absolute value of either displacement is 200 m, so the distance traveled is 200 m in each case. Distances are always positive.

Making sense of the results. In all cases,

if the motion is to the right along a left-to-right real number line, the displacement is positive and if it is to the left, the displacement is negative.

Figure 2-5 illustrates this point.

Related homework: Problems 2-7, 2-8, and 2-9.