you're watching the physics classrooms video tutorial series on kinematics with me mr.
age today's topic is distance versus displacement and what we wish to do today is answer four basic
questions what is distance what is displacement how are these two quantities different than
one another and finally how do you determine the distance in the displacement for any given motion
we're going to begin by talking about distance distance is the amount of ground covered by an
object it's a scalar quantity and when calling something a scalar quantity in physics what we
mean is a quantity that is ignorant of direction it's fully described by magnitude alone magnitude
or numerical value no distance is a scalar and because it's a scalar it's going to ignore any
sort of direction change so here's an example where we have to use this concept of distance
in order to solve a problem it's about reverse reverse walk six meters east and then four meters
west and we want to know what's the distance so when trying to find the distance we just need
to know how much ground did reverse walk over r-e walk six meters and four meters and that
sums up to a total distance walk of 10 meters so Ria's walked a distance of 10 meters that's
the depth mod of ground that's covered by Rhee now when solving this question what we noticed
we ignored that direction change that occurred after the first six meters segment of motion
that's because distance is a scalar it's ignorant of the direction and then man or whether ReWalk
six meters east and then four meters east or six meters east and four meters west distance
is ignorant of direction so it does not affect the outcome of what the answer is if there's
a direction change now we're going to begin our discussion of the topic of displacement
displacements define it as the overall change in position of an object you find out what its
initial position is if I doubt what its final position and you determine the overall change
displacement is a vector quantity and when calling something of vector planning in physics we mean is
a quantity that's fully described by two things magnitude and direction so when calling something
a vector we're saying that it's a direction aware quantity let's look at that same motion
that we had looked at before when we spoke of reverse who walks six meters east and 4 meters
west and now let's ask the question what's the displacement so we need to find the displacement
or the overall change in position we need to find how far is the finished position from the
starting position and if we take these two numbers 6 meters to the right and 4 meters to the left or
east and west what we begin to notice is that that finished position is 2 meters to the east
of the starting position so we have determined how far out of place Rhea is when she finishes
compared to when she starts the overall change in position here is 2 meters to the east that's the
displacement now in this example we're calling 2 meters that magnitude of the displacement and
we're calling East the direction so you see as we express the answer we have to include those
two components of displacement magnitude and Direction like any quantity that's a vector now
in this example one thing that occurs is there's a direction change taking place and displacements
a vector and it keeps track of direction its direction of where and the fact that this means
that we need to consider the 6 meters to the right or 6 meters east to be like a positive 6
in the 4 meters to the left or less to be like a negative 4 so in effect this problem becomes
a subtraction problem it becomes a 6 minus a 4 or a positive 6 plus a minus four and then gives
us a negative two and or a positive two rather than that positive indicates a displacement to
the east displacement is a factor and as such it's aware of these direction change and that's
the one part of the definition that makes displacement quite different than distance
we're going to look a little more at this idea of direction change here we see a person walking
to the right every step to the right takes them a meter further rightward well notice the distance
and displacement are listed there in this this example the person's distance and displacement
always have the same numerical value when we're done 11 meters the distance walked is 11 meters
and the displacement is 11 meters rightward distance and displacement will have the same
numerical value as long as there's no direction change now we're going to look at the same in of
a similar animation but we're going to notice this person this time changes direction and if there is
a direction change what we're gonna notice it's gonna happen right now is we're gonna notice that
the displacement in the distance have different numerical value here as the person walks backwards
he's sort of undoes this forward displacement so maybe walk 7 meters to the right but then after
those 7 meters by walking backwards four more meters to the left that makes the displacement
go down so now it's causing the overall change in position to be less than if he just walked
in one direction so in this situation what we notice is that displacement and distance have
different numerical value because displacement pays attention to that direction change now
we're gonna watch a person walk 2 meters away from where he started as we watch this person walk one
thing we noticed is he doesn't do a direct path from start to finish does a roundabout path and
when doing this roundabout path what we notice is that the distance and the displacement have
different values the distance in this case may be something like 15 meters walks a total distance or
covers a total amount of ground of 15 meters but the overall displacement is 2 meters to the right
so this illustrates the idea of path dependency distance is a path dependent quantity depends on
how you get from start to finish but displacement only depends upon the starting position and the
final position and not up on the path it's not a path dependent quantity now let's look at a
round-trip motion like the one you're watching in on the screen this person is walking 8 meters to
the right or to the east and 2 meters north 8 meters back West and then 2 meters down south
and finishes where they started this is what we mean by a round-trip motion when you finish
exactly in the same position that you started from we might say that in such a situation you
have not had any overall change in position you've not been displaced from the original
position and as such there's no displacement we can say that the displacement for any round-trips
any round-trip motion is always zero now it's your turn to practice here's an example problem can't
decide walks 2 meters east 8 meters west and 4 meters east and you have to determine what is
the distance in what is the displacement so let me give you some time maybe you can pause the video
and take some time to try to solve this question and when you're ready why don't you come back and
check and play the video and see how you did one recommendation why don't you start with a diagram
so here's my diagram for this problem they have a starting point and then I'm I'm drawing out that
the the various lakes of this multi leg truck two meters to the east I'm going to draw that to the
right just like on a map and then eight meters to the last I'm going to draw that to the left just
like on a map and then four meters back to the east and I want to know what's the distance and
what's the displacement so when you do a distance calculation for a multi-link trip you simply add
up all the distances of the legs of the truck so I'm going to take the two the eight in the
four and I'm going to add them up and I end up with 14 meters as the distance travel I do not
need to indicate a direction because distance is a scalar in doesn't regard direction now when it
comes to this place but I do have to consider the directions I have to consider this two to
the right or to the east is a positive to the 8th is a negative 8 and the 4 as a positive 4
and I have to end up the these little distance values but I have to put a plus and minus in
there because displacement is a vector and that plus minus represents east or west so I'm going
to do positive 2 plus negative 8 plus positive 4 and what I've done I get negative 2 meaning the
displacement is 2 meters in the negative direction or off to the west so when we're done here these
are the answers we get 14 meters is the distance and 2 meters west is the displacement so we set
out in this video to try and understand what is the distance and what is displacement and learning
that distance is the amount of ground covered and displacement is the overall change in position of
an object they're quite different based upon their definition and based upon the fact that distance
becomes the quebec quantity that is a scalar in unaware direction and displacement is the quantity
that is very very Direction aware at all times and direction changes have great huge effects of
on displacement and then finally we've learned how to calculate distance and displacement for a very
simple and more complicated multi lake motions well thanks for hanging in till the very end
of this video I like to give you it this time in action plan but before I do give some ideas to how
you can help yourself out we'd like you to maybe help us out a few things you can do to help us
out if you like the video you hate to just press the like button and give us a like or if you think
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if you have a question or a comment go ahead and leave that question or comment now here's
what we can do to kind of help you out an action plan something that you can do next to put all
this into practice and the first idea is that you could go off to our physics interactive section
on our website you'll see the link in that in the description section of this video and then tap on
the kinematics part of physics Interactive's and then go to distance and displacement it's a great
little simulation with some interactive practice for you that's a great first step another great
first step is you could go to our website and go to the concept builder section it's the third
choice on the page and when you go to that third choice pick kinematics and then pick distance
versus displacement concept builder students love concept builders and it's a great way to get some
practice and some follow up to this little video on distance and displacement or if your minds
on physics unit users you could get our app is number one there are three modules on that app
the first module is called kinematic concepts and on the kinematic concepts module mission
K c2 is a great one to do for understanding distance and displacement finally if you just
need a reference we have a tutorial on our website that mirrors some of these video tutorials that
we're doing and you could always use that as a reference thanks for watching enjoy your day