Answer:

Explanation:

Displacement

Displacement

 \[\text{Δ}x\]

is the change in position of an object:

 \[\text{Δ}x={x}_{\text{f}}-{x}_{0},\]

where

 \[\text{Δ}x\]

is displacement,

 \[{x}_{\text{f}}\]

is the final position, and

 \[{x}_{0}\]

is the initial position.

We use the uppercase Greek letter delta (Δ) to mean “change in” whatever quantity follows it; thus,

 \[\text{Δ}x\]

means change in position (final position less initial position). We always solve for displacement by subtracting initial position

 \[{x}_{0}\]

from final position

 \[{x}_{\text{f}}\]

. Note that the SI unit for displacement is the meter, but sometimes we use kilometers or other units of length. Keep in mind that when units other than meters are used in a problem, you may need to convert them to meters to complete the calculation (see Conversion Factors).

Objects in motion can also have a series of displacements. In the previous example of the pacing professor, the individual displacements are 2 m and

 \[-4\]

m, giving a total displacement of −2 m. We define total displacement

 \[\text{Δ}{x}_{\text{Total}}\]

, as the sum of the individual displacements, and express this mathematically with the equation

 \[\text{Δ}{x}_{\text{Total}}=\sum \text{Δ}{x}_{\text{i}},\]

where

 \[\text{Δ}{x}_{i}\]

are the individual displacements. In the earlier example,

 \[\text{Δ}{x}_{1}={x}_{1}-{x}_{0}=2-0=2\,\text{m.}\]

Similarly,

 \[\text{Δ}{x}_{2}={x}_{2}-{x}_{1}=-2-(2)=-4\,\text{m.}\]

Thus,

 \[\text{Δ}{x}_{\text{Total}}=\text{Δ}{x}_{1}+\text{Δ}{x}_{2}=2-4=-2\,\text{m}\text{​.}\]

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