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What I want to do
in this video is

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talk about the difference
between vectors and scalars.

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And they might sound like
very complicated ideas,

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but we'll see over the
course of the videos

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that they're actually
very simple ideas.

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So first I'll give you a
little bit of a definition.

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And then I'll give you
a bunch of examples,

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and I think the examples
will make things super clear.

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Hopefully, they'll make
things super clear.

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A vector is something
that has a magnitude,

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or you could kind of
view that as a size,

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and it has a direction.

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So "and" it has a direction.

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A scalar only has a
magnitude, or size.

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And if that doesn't
make sense to you,

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it will hopefully
make sense to you

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in a second when I
show you an example.

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For example.

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Let's say that I have,
let's say that that's

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the ground-- let me do
the ground in a more

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appropriate ground-like color.

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So this is green
right over here.

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And let's say that
I have a brick here.

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I have a brick on the ground.

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And I pick up that
brick, and I move it over

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to this place right over here.

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So I move the brick
right over there.

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And then I take a ruler
out, and I say, wow,

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I've moved the brick 5 meters.

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So my question to you, is
my measurement of 5 meters,

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is it a vector or a scalar?

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Well, if I just
tell you 5 meters,

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you just know the
size of the movement.

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You just know the
magnitude of the movement.

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So if someone were
to just say 5 meters,

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this is a scalar quantity.

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And when we're referring
to moving something,

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or how much something has, I
guess, changed its position,

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and I don't give
you the direction,

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we're talking about distance.

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And I'm assuming you've
heard the word distance.

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How far of a distance
has something traveled?

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So this is distance.

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So we could say that this
block, or this brick,

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because of my picking
it up and moving it,

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has moved a distance
of 5 meters.

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But if I didn't show
you this picture here,

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and someone just
told you that it

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moved a distance
of 5 meters, you

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wouldn't know if it moved
to the right 5 meters,

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you wouldn't know if it
moved to the left 5 meters,

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if it moved up or
down or in or out,

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or-- You don't know what
direction it moved 5 meters.

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You just know it moved 5 meters.

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If you want to
specify that, so, we

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could say that this
brick right over here,

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that it moved 5
meters to the left.

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Now we have specified a
magnitude, right over there.

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So that is a magnitude.

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And we have specified a
direction, to the left.

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So you now explicitly know that
they went 5 meters to the-- oh,

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sorry.

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It should be 5
meters to the right.

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Let me change that.

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So, 5 meters to the right
is what it got moved.

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It started here and went
5 meters to the right.

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So once again, the
magnitude is 5 meters,

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and the direction
is to the right.

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So what I've just
described to you right here

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is a vector quantity.

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So this, all of this
business right over here,

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this is a vector.

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And when you talk about
the movement, the change

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in position, and you give its
direction, the vector version

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of distance, I guess you could
call it, is displacement.

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So this right here
is displacement.

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So the correct thing
to say, you would

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say that this brick
has been displaced

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5 meters to the
right, or it has been

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moved a distance of 5 meters.

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Distance is a scalar
quantity-- I didn't tell you

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what direction we moved it in.

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Displacement is a
vector quantity.

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We told you that
it is to the right.

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Now let's explore this if
we talk about the actual,

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well, we'll talk about the
speed or velocity of something.

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So let's say that this
5 meters was traveled

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and let's say that
the change in time--

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let me just, because
you're probably not

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familiar with what that means.

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So let's say that the
change in time right here,

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when I moved this
block 5 meters,

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let's say that it
was, I don't know,

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let's say that the change
in time was 2 seconds.

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So maybe right when the
block started moving, maybe

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on my stopwatch it said 0.

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And then on my stopwatch
when it stopped moving,

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it said, or when it
got to this position,

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I should say-- when it
left from this position,

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my stopwatch said 0.

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When it got to this position
my stopwatch said 2 seconds.

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So the change in time, or the
duration we're dealing with,

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is 2 seconds.

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And this is, for all
we know, time only

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goes in the positive direction.

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So you could assume
that it's, you

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could pick that as a vector
or a scalar quantity,

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I guess, because there's
only one direction for time,

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as far as we know, or
at least in what we're

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going to deal with for
the simple physics.

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So what is a measure of
how fast this thing moved?

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So, how fast did
this thing move?

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So we could say it moved
5 meters in 2 seconds.

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Let me write this down.

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So it moved 5 meters
per 2 seconds.

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Or we could write this as
5/2 of a meter per second.

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Or 5 divided by 2 is what?

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5 divided by 2 is 2.5
meters per second.

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This right here is just
the 5 divided by 2,

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let me make that clear.

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That right there is just
the 5 divided by the 2.

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So my question to you.

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This 2.5 meters per
second tells you

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how far it traveled in a
certain amount of time.

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Is this a vector or
a scalar quantity?

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It is telling you
how fast it went,

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but is it giving you just
a size of how fast it went?

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Or is it also giving
you direction?

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Well, I don't see
any direction here.

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So this is a scalar quantity.

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And the scalar quantity for
how fast something is going

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is speed.

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So we could say that
the speed of the brick

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is 2.5 meters per second.

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Now, if we do the
same calculation,

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and we say it went
5 meters-- I'll just

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write m for meters-- to the
right in 2 seconds, then

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what do we get?

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We get 2.5, once again, 2.5
meters per second-- I'll

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just abbreviate them as meters
per second-- to the right.

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So is this a vector
or a scalar quantity?

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I'm telling you the magnitude
of the speed, that's right here.

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This is the magnitude,
2.5 meters per second.

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And I'm also telling you
the direction, to the right.

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So this is a vector quantity.

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This is a vector quantity.

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And when you specify both
the speed and the direction,

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so the 2.5 meters per second
is a scalar, and the direction,

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you are talking about velocity.

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You are talking about velocity.

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So an easy way to
think about it,

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if you're thinking
about change in position

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and you specify the direction
of the change in position,

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you're talking
about displacement.

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If you're not talking
about the direction,

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you want the scalar version,
you're talking about distance.

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If you're talking about how
fast something is going,

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and you give the direction
that it's going in,

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you're talking about velocity.

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If you don't give the direction
you are talking about speed.

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Hopefully that helps
you a little bit.

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In the next video,
we're going start

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working with these a
little bit to start

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solving some basic questions
about how fast something

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is going, or how
far it might travel,

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or how long it might
take it to get someplace.