- [Instructor] Previous videos
we've talked a little bit about distance traveled
versus displacement.
What I'm gonna do in this video is discuss it
on a one dimensional number line.
And we'll get a little bit more mathy in this video.
So here is my number line.
Let's say that this is a zero,
one, two
three,
four and it keeps going on
and then in the negative direction,
negative one,
negative two,
and negative three.
And let's say that I start off
with a lemon.
Let's say my lemon starts off right over here at zero
on my number line.
And let's say it first moves two to the right
so at first moves two to the right.
I'll denote that by plus two
and then from there, it moves
three to the left
and then it moves three to the left.
And I will use negative for the left.
So it moves three to the left.
And then let's say that it then
moves
another one to the left.
So then it goes another one to the left
and I'll denote negative one
as moving one to the left.
So based on what we know about distance traveled
and displacement,
what is the distance traveled for this dot?
Distance traveled.
Pause the video
and see if you can figure that out.
Or remember,
distance traveled is the entire path length.
Or the entire length of the dot's journey.
So this is going to be equal to
two to the right.
So plus two
and then three to the left.
Now this is an important notion.
When we talk about distances,
we wouldn't say positive or negative.
We just care about the absolute value of
the amount that we are traveling.
So we won't specify a direction.
Now you might say, "hey,
"where is the direction being specified?"
well implicitly, whether something is positive or negative
on this number line
is giving a direction.
But if we're talking about distances,
we wouldn't pay attention to the direction.
We only care about the magnitude.
So this would be two
plus three
plus one.
Doesn't matter if this is one to the left
or one to the right.
Doesn't even matter if it's positive one or negative one.
We care about its absolute value.
We care about its magnitude.
So the distance traveled in this example
is going to be six units.
Whatever the units are on my number line right over here.
If these are in meters
then this would be six meters.
Now what is the displacement?
Now remember, displacement is net change in position.
Displacement.
What is that going to be?
Pause the video and see if you can figure it out.
Well displacement is going to be
you could view this as equal to
your final position
and we'll use X.
Let's say this is the X-axis.
So we'll say X final, your final position
minus your initial position.
It's really just your change in position!
So what is your change in position here?
Well your final position is
you are at negative two at x equals negative two.
And then what was your initial position?
Your initial position, you started at zero.
So negative two minus zero is equal to negative two.
So how would we visualize that on our drawing here?
Well we started here.
Just think about what is your net change in position?
You started here.
And regardless of what your path was,
you ended up two to the left.
So your
your displacement is negative two.
Now displacement, we care
not just about the magnitude.
We care about the magnitude and the direction.
So you might be saying, well,
where is the direction specified
if I just say negative two?
Well, the sign in a one dimensional case
is giving us our direction.
So the sign is giving us a direction.
I started off implicitly with this notion
that negative is to the left
and positive is to the right.
And we're in this one dimensional world.
And those are the only two directions that I can travel in.
So if I'm in this one dimensional world
or if I'm thinking about just one dimension,
the sign gives me my direction.
So that's why displacement
where I care about the magnitude and the direction,
I do care about the sign.
While distance,
where I only care about the magnitude,
I don't care about the sign.
So I just keep adding up the magnitudes
while over here, another way you can think about it,
you first get displaced by two to the right
so that's plus two.
The plus says to the right.
Then you get displaced by three to the left.
So that is minus three.
And then you get displaced by one to the left again.
So that's minus one.
That's why we're talking about displacement.
That's why we care about the sign.
And if you are to add all of these together,
you are going to get a net displacement
of negative two.
But an easier way was just what's your final position
minus your initial position?