Video: Distance Versus Displacement

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Distance Versus Displacement

Video Transcript
What is the difference between distance and displacement?
When are these two quantities the same value and when are they different?
And how do you calculate distance and displacement for a back-and-forth motion?
Hi. I'm Mr. H. and I have some answers for you.
The Difference
For an object that is moving along the ground, the distance is defined as the amount of ground that is covered. Distance is a scalar quantity. Scalar quantities are fully described by a magnitude or numerical value. Displacement is different. It is defined as the overall change in position. Displacement is a vector quantity. It is described by both a numerical value (a magnitude) AND a direction. While a scalar like distance is direction-ignorant, a vector like displacement is direction-aware.
This animation of a man walking along the ground demonstrates the difference between distance and displacement. The man walks a distance of 16 meters. He finishes 2 meters east of his starting place. He is dis-placed 2 meters to the east. When there is a change in direction, distance and displacement have different numerical values.

Example 1
To further illustrate the difference, consider this back-and-forth motion. 
Noah decides to grab a snack at Mickey D's. His friend Samir wants to come with. Noah drives 3.2 km West to Samir's house. Samir hops in the car. Noah then drives 2.0 km, East to Mickey D's. What is Noah's distance? What is Noah's displacement?
Distance is ignorant of direction. To determine the distance, ignore all directional information. Distance refers to the amount of ground that Noah drove over. Simply add the lengths of the two parts of the back-and-forth trip. Noah traveled a distance of 5.2 km.

Displacement is quite different. It is direction-aware. For displacement, it matters that the 3.2 km was in the West direction and that the 2.0 km was in the East direction. To determine the displacement, consider one of these to be positive and the other to be negative. There is no right or wrong way to do it.  Let's just say that East is positive and West is negative. We can conclude that the overall change in position is (-3.2 km) + (+2.0 km). That's a displacement of -1.2 km. But wait! What's the negative mean? Well we started by saying that West is negative. So this is a displacement of 1.2 km, West.

Example 2
Allow me to walk through a more difficult example and then I will provide you with some Tips for Success.
Noah gets an urge to go to Mickey D's for lunch. His friends Kaylin and Waylon want to go along. So Noah leaves his house and drives 1.4 km, East to pick up Kaylin. Then Noah drives 3.6 km, West to pick up Waylon. And finally, Noah drives 1.0 km, East to Mickey D's. What is Noah's distance? What is Noah's displacement?
Distance is direction-ignorant. So determining distance means we just add up all the individual distances. The distance is 1.4 km + 3.6 km + 1.0 km. Noah drives a total distance of 6.0 km. That's the amount of ground that is covered.
Displacement is the direction-aware quantity. It pays attention to the direction of each leg of this trip. I'm going to begin by designating a + and a - direction. I'll say East is +. That makes West -. Now use this + and - as directions and add the three individual displacements to find the overall displacement. 
+1.4 km + (-3.6 km) + (+1.0 km) = -1.2 km
The result is negative, which means the overall displacement is directed to the West. So Noah's displacement for this 3-leg trip is 1.2 m, West

Tips for Success
Now for a few Tips for Success. Calculating distance and displacement for a back-and-forth motion involves applying the definitions of the two terms. Begin the process by sketching a diagram. Draw vector arrows in the appropriate direction and having the relative length. Label them with numbers. Second, for Distance, just add up all the numerical values. Ignore direction becasuse distance is a scalar. For Displacement, begin by defining the + and the - directions. Then translate direction information into a + and -. Then add up all these numbers with their +/- direction signs included. When done, translate the +/- sign back into a direction.

In the Description section of this video, you will find links to some awesome interactive exercises on our website. Putting this information to practice is a great way to ensure that You Got This!
I'm Mr. H. Thanks for listening!


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