What I want to do in this video is talk about the difference

between vectors and scalars.

And they might sound like very complicated ideas but we'll see over the course of the videos

that they're actually very simple ideas.

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

and then I'll give you a bunch of examples

and I think the examples will make things super clear.

Hopefully they'll make things super clear.

A vector is something that has a magnitude -

or you can kind of view that as a size -

and it has a direction.

So, and it has a direction. And it has a direction.

A scalar only has a magnitude or size.

And if that if that doesn't make sense to you

it will hopefully make sense to you in a second when I show you an example.

For example: let's say that I have a

that's the ground right there -

let me do the ground in a more appropriate ground-like color.

So, this is green right over here...

And let's say that I pick and I have a brick here

I have a brick on the ground.

And I pick up that brick

and I move it over to this place right over here.

So I move the brick right over there

and then I take a ruler out and I say,

"Wow, I have moved the brick five meters."

So my question to you: is my measurement of five meters

is it a vector or a scalar?

Well if I just tell you five meters, you just know the size of the movement.

You just know the magnitude of the movement.

So if someone were to just say "five meters", this is a scalar quantity.

When we're referring to moving something

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

and I don't give you the direction, we're talking about distance.

and I'm assuming you've heard the word distance

How far of a distance has something traveled?

So this is distance.

So we can say that this block or this brick because of my picking it up and moving it

has moved a distance of five meters.

But if I didn't show you this picture here

and someone just told you that it moved a distance of five meters,

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

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

or if it moved up or down or in or out -

you don't know what direction it moved five meters,

you just know it moved five meters.

If you want to specify that,

we could say this brick right over here moved five meters to the left.

Now we have specified a magnitude - right over there, so that is a magnitude -

and we have specified a direction: "to the left".

So you now explicitly know that it went five meters to the le-

oh, sorry, it should be five meters to the right, let me change that.

So five meters to the right is what it got moved to.

It started here, it went five meters to the right.

So once again:

the magnitude is five meters

and the direction is to the right.

So what I've just described to you right here is a vector quantity.

So all of this business over here - this is a vector.

And when you talk about the movement, the change in position, and you give its direction -

the vector version of distance, I guess you could call it -

is displacement.

So, this right here is displacement.

The correct thing to say:

you would say that this brick has been displaced five meters to the right,

or it has been moved a distance of five meters.

Distance is a scalar quantity.

I didn't tell you what direction we moved it in.

Displacement is a vector quantity.

We told you that it is to the right.

Now let's explore this, if we talk about the actual speed or velocity of something.

So let's say that this five meters was traveled,

and let's say that the change in time

(let me, just... because you're probably not familiar with what that means)

Let's say that the change in time right here - change in time

when I moved this block five meters

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

So maybe right when the block started moving

maybe on my stopwatch it said zero

and then on my stopwatch when it stopped it stopped moving it said -

or when it got to this position, I should say -

When it left from this position my stopwatch said zero,

when it got to this position my stopwatch said two seconds.

So the change in time or the duration we're dealing with is two seconds.

For all we know, time only goes in the positive direction,

so you can pick that as a vector or a scalar quantity I guess

because there's only one direction for time as far as we know

or at least in what we're going to deal with for the simple physics.

So what's a measure of how fast this thing moved?

How fast did this thing move?

So we could say it moved five meters in two seconds.

Let me write this down

So it moved five meters per two seconds.

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

or five divided by two is 2.5 meters per second.

This right here is just the five divided by two.

(let me make that clear)

That right there is just the five divided by the two.

So my question to you:

this 2.5 meters per second - it tells you how far it travelled in a certain amount of time -

is this a vector or a scalar quantity?

It is telling you how fast it went,

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

Well I don't see any direction here

so this is a scalar quantity.

And the scalar quantity for how fast something is going is speed.

So we could say that the speed of the brick is 2.5 meters per second.

Now if we do the same calculation, if we say it went five meters -

I'll just write "m" for meters -

five meters to the right in two seconds.

Then, what do we get?

We get 2.5 meters per second -

I'll just abbreviate them -

as meters per second to the right.

So is this a vector or a scalar quantity?

I'm telling you the magnitude of the speed that's right here - this is the magnitude:

2.5 meters per second -

and I'm also telling you the direction: to the right.

So this is a vector quantity.

And when you specify both the speed and the direction -

so the 2.5 meters is a scalar and the direction -

you are talking about velocity.

So, easy way to think about it:

If you're thinking about change in position

and you specify the direction of the change in position you're talking about displacement.

If you're not talking about the direction, you want the scalar version,

you're talking about distance.

If you're talking about how fast something is going

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

you're talking about velocity.

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

Hopefully that helps you a little bit -

and in the next video we're going to start working with these a little bit

and start solving some basic questions

about how fast something is going or how far it might travel

or how long it might take it to get someplace.

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