 # Distance & Displacement

This post will take a look at distance and displacement—two core ideas in classical physics.

To understand concepts such as distance and displacement, you first need to understand position. Position is the location of an object. When we are speaking of distance and displacement, this involves an object changing position. However, an object can only change position if it is relative to something else. For example, if a person walks 5 meters from their bedroom to the kitchen, this distance can only exist because there are two positions

• The bedroom
• The kitchen

The position of the person is defined by what we call a reference frame. The reference frame is a stationary object from which position is determined. In the example above, there are three positions

• The bedroom
• The kitchen
• The walking person

The bedroom is the reference frame. In other words, wherever the walking person goes, their position is measured in relation to the bedroom. The kitchen is simply the goal destination or where the walking person is going.

Distance

Distance is a measure of the length of the path between a person’s initial and final position. In our walking example, the person traveled 5 meters from the bedroom to the kitchen. This 5 meters is the distance.

bedroom walk 5 meters to the kitchen

Displacement is a little more complicated. Displacement is the net change in position. In other words, displacement compares your final position to your initial position and determines if there is a difference in these values. For example, if we use the walking example again, the displacement is the same as the distance. This is because the person walked 5 meters and did not move anymore. Doing some simple math, we can calculate the displacement as shown below

Final position – original position = displacement

5 – 0 = 5

The person traveled 5 meters to the final position of the kitchen. The original position is 0 meters because the bedroom is where the person started at and is the reference frame.

The value of the distance and the displacement are not always the same. For example, if the walking person goes to the kitchen and then returns to the bedroom, we get the following numbers

bedroom walk 5 meters to the kitchen

Kitchen walk 5 meters to the bedroom

The distance travel here is 10 meters as we went 5 meters to the kitchen and 5 meters back to the bedroom. However, the displacement is zero because our final position and our initial position are the same in that we left the bedroom and came back to the bedroom. There was a change in the distance but not in the person’s position when the walking was over.

Scalar and Vector

Distance is a measure of magnitude (amount of) length. In this situation, only the magnitude is being measured, so this is a scalar quantity. In the example above, the person walked 5 meters. We know the direction, but this is not needed to understand that the person walked 5 meters

Displacement is a measure of magnitude and also direction. When magnitude and direction are considered, it is called a vector quantity. In our example above, the person walked to the kitchen and then walked backed to the bedroom. Walking to the kitchen could be considered a positive distance while walking back to the bedroom would be regarded as a negative distance. This is why the displacement is zero in the second example. Walking back and forth essentially cancels the values out.

This examination of motion is called kinematics, which is the study of motion without being concerned with what causes this motion.

Conclusion

Distance and displacement are foundational concepts in physics on which many other complex ideas are built upon. Therefore, understanding how things move in relation to space is critical to appreciate for students studying this subject.

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