# displacement is the change in velocity of an object

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### Displacement

If an object moves relative to a frame of reference—for example, if a professor moves to the right relative to a whiteboard—then the object’s position changes. This change in position is called displacement. The word displacement implies that an object has moved, or has been displaced.

Although position is the numerical value of x along a straight line where an object might be located, displacement gives the change in position along this line. Since displacement indicates direction, it is a vector and can be either positive or negative, depending on the choice of positive direction. Also, an analysis of motion can have many displacements embedded in it. If right is positive and an object moves 2 m to the right, then 4 m to the left, the individual displacements are 2 m and −4−4 m, respectively.

## ΔxΔx means change in position (final position less initial position). We always solve for displacement by subtracting initial position xx0 from final position xfxf. 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.

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 −4−4 m, giving a total displacement of −2 m. We define total displacement ΔxTotalΔxTotal, as the sum of the individual displacements, and express this mathematically with the equation.

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where ΔxiΔxi are the individual displacements. In the earlier example,

Δx1=x1x=2=2m.Δx1=x1−x0=2−0=2m. Δx2=x2x1=−2(2)=−4m.Δx2=x2−x1=−2−(2)=−4m.

Thus,

ΔxTotal=Δx1+Δx2=24=−2m​.ΔxTotal=Δx1+Δx2=2−4=−2m​.

The total displacement is 2 − 4 = −2 m along the x-axis. It is also useful to calculate the magnitude of the displacement, or its size. The magnitude of the displacement is always positive. This is the absolute value of the displacement, because displacement is a vector and cannot have a negative value of magnitude. In our example, the magnitude of the total displacement is 2 m, whereas the magnitudes of the individual displacements are 2 m and 4 m. xixi, we assign a particular time titi. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity vv–. This vector quantity is simply the total displacement between two points divided by the time taken to travel between them. The time taken to travel between two points is called the elapsed time ΔtΔt.