Distance vs. Displacement

Continuing on in my posts in Introductory Physics, here I want to explain the difference between DISTANCE and DISPLACEMENT.

First of all, Distance is said to be a "scalar" property, which means that it is a quantity that has no direction associated with it, and is defined only by its magnitude. (Another scalar property is mass... all magnitude, no direction.) Conversely, Displacement is a "vector" property, which means that in addition to its magnitude, it also has a relative direction. (Another vector is velocity... it is defined by a magnitude AND a direction.)

With those definitions, we can differentiate distance and displacement even better. Imagine walking to school in the morning. The number of footsteps you have to take to arrive at school (the magnitude) describes the distance (maybe not the most convenient units, mind you!). If your school is straight up the street, or if you have to take a winding path through the park and over the tracks, the number of steps defines the distance... Direction is irrelevant in explaining the distance. You can walk 100 meters in a straight line, or 1000 meters turning left, right, left, and back again. The measured path you travel is the Distance.

On the other hand, Displacement DOES have direction associated with it. If you are going to school one day, and you go straight there, 100 meters up the street, your displacement is 100 meters North (or whatever direction). Now, on the next day, you have a doctor's appointment first, you have to drive 2000 meters up the street (past your school), and then afterwards you drive back the 1900 meters to your school. The DISPLACEMENT is 100 meters, because you end up 100 meters North of where you started. It doesn't matter the path you take to get there. You could travel around the world and back again, and you would still be displaced 100 meters from where you started. The DISTANCE, however, which has no direction but is just the footsteps (or whatever) you traveled, is much larger. On the first day, the distance is 100 meters. On the second day, you travel 2000 meters plus 1900 meters back, which is 3900 meters.

In summary, think of distance as the path taken to get somewhere, and describe it as some quantity without direction (eg. 50 meters away). Displacement is simply the difference between where you start and where you end, no matter the path taken, but considering the overall direction moved (eg. 25 meters to the right).

Hopefully that helps to explain Distance and Displacement. Drop me a line if you would like any more discussion.