If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Intro to vectors and scalars

AP.PHYS:
INT‑3.A (EU)
,
INT‑3.A.1 (EK)
,
INT‑3.A.1.1 (LO)
,
INT‑3.A.1.2 (LO)
,
INT‑3.A.1.3 (LO)

## Video transcript

what I want to do in this video is talk about the difference between vectors 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 a magnitude and or you could kind of view that as a size and it has a direction so and and it has a direction and it has a direction a scalar only has a magnitude or size and 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 let's say that 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 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've moved the brick I have moved the brick five meters 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 five meters this is a scalar quantity scalar quantity and when we're referring to moving something or 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 could 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 move to the left five meters if it moved up or down or in or out or you don't know what direction it moved five meters you just know it moved five meters if you want to specify that so we could say that this brick right over here that it moved five five meters to the five meters to the left to 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 they went five meters to the oh sorry it should be five meters to the right let me change that so five meters to the to the that's why the direction to the right is what it got moved FiOS started here it went five meters to the right so once again the magnitude is five meters and in the direction is to the right so what I've just described to you right here is a vector quantity so this all of this business right 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 displacement so 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 well we'll talk about the speed or velocity of something so let's say that my let's say that my that this five meters was traveled and let's say that the change in time let's say that the change in time and when I let me just because you're probably not familiar what that means so let's say that the change in time right here change in time when I moved this block five meters let's say that it was I don't know let's say that this the change in time was two seconds so maybe right when I when the block started moving maybe on my stopwatch it said zero and then on my stopwatch when 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 and this is you know for all we know time only goes in the positive direction so you could you know you could assume that it's what you could you could pick that as a vector or scalar quantity I guess because there's only one direction for time as far as we know or at least in that what we're in what we're going to deal with for the the simple physics so what is so what's a measure of how fast this thing moved so 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 it moved five meters per 2 seconds per 2 seconds or we could write this as five halves of a meter per second or 5/2 is what 5/2 is 2.5 meters per second meters per second meters per second this right here is just the 5/2 let me make that clear that right there is just the 5 divided by the 2 so my question to you this 2.5 meters per second tells you how how far it traveled in a certain amount of time is this a vector or a scalar quantity it is telling you how fast into it but is it giving you just a size of this of how fast it went or is it also giving you direct well I don't see any direction here so this is a scalar quantity and the scalar quantity for how fast something is going 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 we say it went to if we say it went 5 meters 5 I'll just write em 4 meters 5 meters to the right in 2 seconds in 2 seconds then what do we get we get 2.5 once again 2.5 meters per second I'll just abbreviate them as meters per second meters per second to the right to the right so is this a vector or scalar quantity I'm telling you the the the magnitude of the speed that's right here this is the magnitude two point five meters per second and I'm also telling you the direction to the right so this is a vector quantity this is a vector quantity and when you specify both the speed and the direction so the two point five meters per second is a scalar and the direction you are talking about velocity 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 that helps you a little bit in the next video we're gonna start working with these a little bit to start solving some basic basic questions about how fast something is going or how far it might travel or how long it might take it to get someplace