Distance and displacement introduction

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 ten kilometers to the east ten kilometers east and then it takes a right turn and then it goes five kilometer south five kilometers south and then it takes another right turn and it goes ten kilometers west ten 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 all right 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 ten kilometers plus five kilometers plus five kilometers plus ten kilometers plus ten kilometers which would give us 25 kilometers that would be 25 kilometers so some of y'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 that it ends up right over here at the end of its journey and so it's change in position is it would have moved a net 5 kilometer 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 kilometres 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 kit situation five kilometres 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 a the the entire path and this thing will never be negative you could travel zero kilometers but as long as you are 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