Main content

## Distance, displacement, and coordinate systems

# Distance and displacement introduction

## Video transcript

- [Instructor] So let's
say we have a sheep and it is hungry. So that is my sheep. My best, quick drawing of a sheep and it is just following the grass wherever it finds good grass to eat and so in pursuit of tasty grass, it first goes 10 kilometers to the east, 10 kilometers east and then it takes a right turn and then it goes five kilometers south, five kilometers south and then it takes another right turn and it goes 10 kilometers west, 10 kilometers west. My question to you is how
far has this sheep traveled? And pause the video and see
if you can figure that out. How far has that sheep traveled? Alright, now let's try
to answer this together and it's a little bit of a trick question because depending how
you interpret the idea how far something has traveled, there could actually be
two valid answers here. One answer is you could say what is the total distance traveled? So let me write this one down. This is an important concept. Distance traveled and this would be the
total length of its journey or the total length of its path. So the distance traveled in this situation would be 10 kilometers
plus five kilometers, plus five kilometers plus 10 kilometers, plus 10 kilometers which
would give us 25 kilometers. That would be 25 kilometers. So some of you all might have said that the sheep traveled 25 kilometers. If that's what you came up with, what you calculated is the
total distance traveled. Now, some of you might have
said, wait, hold on a second, the sheep was here before and then it ends up right over here at the end of its journey and so its change in position
is it would have moved a net five kilometers south. From this point to this point would have been five kilometers south. It doesn't matter what
it did along the way, what its path was. At the end of the day, it
ended up five kilometers south of where it started out and
this would also be a valid way of saying how far it traveled and this notion is known as displacement. So the displacement would
be in this situation five kilometers south. So pause this video. What do you think is the
definition or the difference between saying the
distance something traveled versus its displacement? Well, as we mentioned, the
distance something travels is the entire length of its journey. It's the entire path and this
thing will never be negative. You could travel zero kilometers
but as long as you are, your position keeps changing,
this thing will only increase because it's the total
length of your path. Your displacement is
your change in position and since it's a change in position, not only will we mention
the five kilometers, we'll say in what direction. The position of the sheep
has changed five kilometers to the south. So let me write this down. This is total length of path, total length of path is
the distance traveled while the displacement is
the change in position, change in position.