2. 1D Motion / Kinematics

Vectors, Scalars, & Displacement

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concept

## Introduction to Vectors and Scalars

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Hey, guys. So in this video, I'm gonna introduce you to two types of measurements that you'll need to know called vectors and scale er's Let's check it out. So whenever we take measurements in science, we're always gonna get the magnitude. For example, let's say you take a thermometer outside and you measure the temperature to be F, or you measure a box and your way to be 10 kg. The magnitude is really just the size of the measurement. You can think about the size as just the number, and so the size or the number of the measurement is the magnitude at 60 and the 10 and then just have the units. But some measurements are a little bit more specific. Some measurements also give us direction. For example, let's say you're describing where you walked outside and you say I walk 10 m to the right or let's say you're describing where you're driving and you say you're going 20 miles an hour to the north. So both of those things are examples of direction. And so let's go through a bunch of examples to make this stuff really, really straightforward. So let's say you weigh in apple in it weighs 5 kg. You're measuring the quantity of mass. The 5 kg represents the magnitude, but it doesn't make sense to ask which direction those 5 kg go, so we don't have direction there. What about days, days or 24 hours long? So we're measuring a time there her 24 hours or magnitude, but it doesn't make sense to ask which direction Those 24 hours ago. Now we already talked about this one. It's 60 degrees outside, so 60 degrees is a measurement of temperature and we have the magnitude. But it doesn't make sense to ask which direction to those 60 degrees go in. So we don't have direction there now for this last one here, I pushed with 100 Newtons to the left. When you're pushing something, you're measuring the force. The 100 Newtons is the magnitude, and here it actually does make sense to ask which direction you're pushing that could affect things. Are you pushing the box or whatever you're pushing to the right to the north, to the left. So here we do have a direction. And so, in physics measurements with direction are called vectors. So, for example, force has magnitude and direction. So it is a vector, whereas measurements without direction are called scale er's. So, for instance, mass time and temperature since they have magnitude on Lee and not the direction these air examples of scale er's. So let's take a look at to sort of related ideas or related measurements. I walked for 10 ft, so let's say you talk to your friend. You said I walked for 10 ft so that you have the measurement right here. That's the magnitude. But you're not specifying which direction you went in. You could have gone five to the right five to the left. You could have gone 10 and whatever direction. And so we don't have the complete idea of that measurement, whereas now let's say you talk to your other friend, you say, Well, I walked 10 ft towards the east direction, so now you have the magnitude and the direction, so we know that this one's gonna be the vector, and this one is going to be the scaler. And so in physics, there's two special words for these measurements. I walked for 10 ft, is called the Distance the scaler version of it. Whereas the more complete picture, the vector is called The displacement. And both of these words here answer the question. How far did you go? Now let's take a look. The last two I drove for 80 MPH or I drove for 80 MPH to the west. So 80 MPH is our magnitude, but doesn't give us the direction. You could have gone 80 MPH to the south, to the west, east, North you don't have with the direction is versus this sentence over here I drove 80 MPH to the west. Gives us more information and more complete idea of what that motion or measurement is. You have magnitude and direction. So just like the other two, this one's gonna be vector, and this one is gonna be the scaler. And we have two special words for these measurements as well. This one, that scaler is gonna be called the speed and the vector is gonna be called the velocity. Both of these words here answer the question. How fast did you move or did you go and, um, the other thing to remember is that or one thing to make? The easy to remember is that the velocity V is the vector and speed with s is the scaler So v with the s with s Hopefully guys, I painted a really, really clear picture of the difference between vectors and scholars. So that's it for this one.

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## Displacement vs. Distance

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Hey guys in previous videos, we talked about the difference between vectors and scholars and we use displacement and distance as examples of vectors and scholars. We said that there were two similar sounding words to describe how far something moved. And so we're measuring the quality of length. So in this video I'm gonna talk about the difference between those and more importantly, I'm gonna show you how to calculate each one of these things. So let's check it out. Let's actually just take a look at this example over here. Let's say you had some kind of measuring tape, a ruler and you went 10 m to the right and six m to the left. Well, there's two different numbers that you can get out of these two motions tend to the right and six to the left. And the basic idea is that the distance which is represented by the letter D is just the total of all the motions that you do. It's the total of all the links traveled. Whereas the displacement on the other hand is a little bit more specific. It's a change in your position in physics. Your position is just where you are on this number line here. It's represented by the letter X. And one way you can think about the displacement is that it's the shortest path between your initial and final positions. Your initial position is just X. Not your final position is X. Easy to the two symbols that you'll see. So, and this number line here, you started off at X not and you ended off at X. And the shortest path is just the arrow that connects those two things. So this right here is your displacement. So let's talk about the numbers in this specific example. So you went 10 to the right and six to the left. And the total of all the links that you travel is just 10 plus six and that's 16 m. So notice how this measurement also doesn't have a direction, it's just a magnitude only, so it's a scalar. Whereas the displacement is really just how far you've actually changed from where you started to ending how far you actually moved. Well you went you went 10 to the rights and you went six backwards. So that means you ended up at four, Whereas your initial position was zero. So your displacement is just 4 0 which is four m to the rights. Another way you can think about this also is that you went 10 and then six backwards. So you also get four. Notice how this measurement has a magnitude and a direction. So it's a vector. So now let's talk about the equations when you're calculating the distance or the total distance, you're just going to add up all the lengths or all the distances and there could be many more than two. So for example, this was D one, this is 10, this is D two which is six and then you ended up with 16. Whereas your displacement delta X. Which gets a little arrow on top of it because it's a vector. It's gonna be your final minus your initial position over here. And that's really all there is to it guys. So let's go ahead and take a look at some examples down here we're gonna be calculating the displacement and the total distance from A. To B. For each of these situations. So we're gonna have X equals negative two and then X final equals seven. So the shortest path is that arrow that connects them. And so delta X. Is just X final minus X. Initial. So it's just gonna be seven minus negative two. So be careful with the negative sign, you're gonna add those two things together and we're gonna get plus nine m to the right. So for the distance the total distance traveled, that's going to be all the distances involved over here. The green multiple. And really there's just one total distance that you travel D. Is just nine you went to and then seven this way right so it's two to go to zero and then seven in deposit directions. The whole thing is nine. So that means that your total distance it's just nine. So notice how these two numbers are the same and that's perfectly fine. They absolutely can be the same number. Let's check out the next example. So now we're actually going to the left in this case. So that's important. We're going from seven all the way to three. So our displacement delta X. Is X. Final minus X. Initial our X final is three. Rx initial is seven. And so our displacement is negative four m. So this is also going to be to the left. So the negative sign or to the left also just means the same thing. Negative signs. Um Yeah so that just means the same thing. And so your distance over here, your total distance is just again D one D. Two And so on and so forth. Well there's only only one distance that we traveled from 7-3 but the distance is always going to be positive and that's just four. So that means that our total distance is four m. Notice how this is positive because the direction doesn't matter just the total length traveled. Whereas this has a negative sign because it has a direction. And so finally let's take a look at our last example. We're gonna move from four all the way to 10 but then we're actually gonna move back to where we started from. So what is the total displacement, DELTA X. It's X final minus X. Initial my initial position was actually four. I went to 10 but then I went all the way backwards. So that means that I actually ended up right over here. This is my final position at four. So my final minus initial is just 4 -4 which is just zero. In other words I haven't displaced anywhere because I went forward and it came back to where I started from. But what about the total distance? Well, this is gonna be D one and D two and so on and so forth. This first distance over here is actually six because I'm going from 4 to 10. The second one I'm going to 10 to 4 is also another six. So this is also six. So let's call that D to its call this D one. And so this is just gonna be D total is six plus six is 12. So even though you literally walked 12 m, you've actually displaced nothing because you ended up back to where you started from. So this is the distance and that's the displacement. So really the displacements can sometimes be negative as we've seen before as we've seen here in these examples, but distances are always going to be positive. And in physics these positive and negative signs are usually just used to indicate the direction. For example, we got negative four m and that just means that we were going to the left here, we got positive nine m. That just means we're moving to the right, that's it for this one. Guys, let me know if you have any questions

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Problem

ProblemStarting from a pillar, you run a distance 140m east (the + x-direction), then turn around.

(a) How far west would you have to walk so that your total distance traveled is 300m?

(b)What is the magnitude and direction of your total displacement?

A

(a) 160 m,

(b) 20 m, west

(b) 20 m, west

B

(a) 160 m,

(b) 20 m, east

(b) 20 m, east

C

(a) 580 m,

(b) -300 m, west

(b) -300 m, west

D

(a) 440 m,

(b) -300 m, east

(b) -300 m, east

Additional resources for Vectors, Scalars, & Displacement

PRACTICE PROBLEMS AND ACTIVITIES (27)

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- FIGURE EX1.8 shows the first three points of a motion diagram. Is the object's average speed between points 1 ...
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