 Hello everybody and welcome to Tutor Terrific. This is going to be the first video in a chapter two unit two set of videos from physics course. We are going to look at one-dimensional motion, so it's one-dimensional kinematics. I'll go over that definition later in these set of videos. We're going to look at reference frames and how we position things, displacement, and we're going to look at scalars versus vectors. So what we're going to look at in this chapter and many chapters here on out are objects in motion. Now objects in motion require a lot of mathematics to study and a lot of terms to define. So while that might seem daunting to you, it's not. I promise you you will get used to this very quickly. Let's start with the most important definition for the next few units kinematics. Kinematics is the study of the motion of objects. We're looking at objects while they're in motion, while they're moving. Then we can look at many, many quantities involved to describe that motion. We're describing the motion that exists. I want to show you here a small sort of graphic that organizes the topics in physics. I can show you where kinematics falls in the study of physics in general. Physics has lots of topics in this first row here, optics, mechanics, electricity, and heat. We are studying mechanics specifically kinematics. So we're describing the motion. Later on we're going to look at dynamics, but for right now this is kinematics and this is where we're kind of falling in the whole hierarchy of studies in physics. Alright now in one-dimensional motion we have to go over this particular quantity right here, this object. It's called the number line and the number line is where we live when we're in one dimension. It's the way we measure all the quantities I'm going to define in the next few lessons. Now the number line, as you know, is often listed with integers, negative ones on the left of zero, and positive ones on the right of zero. And you also know that often in the Cartesian coordinate plane, which we're not working in right now, you can have a number line going vertical. Well when it comes to one-dimensional physics you can have a single number line as the place you live, either horizontal or vertical like this. But you must define what I call a reference point. The reference point is some position on the coordinate system that acts as, well I'll call it the zero basis for all other measurements to be compared. What I mean by zero basis is everything is referenced to this particular place I call zero. And for this number line right now, as you could see, I've numbered this as zero. But the reference point doesn't need to be at what you call zero. The reference point can be anywhere. I can reference home measurements with respect to this red dot down here instead of this one. So that's what is known as a reference point and nothing makes sense unless you have one. All of your measurements make no sense unless they are thought of as with respect to some reference point. So position is where this whole conversation is going to right now. Position is specifically an object's location with respect to the origin or the reference point. We often label positions with an X, like this script X here. So I'm going to say that this number line is measuring distances in meters from the reference point zero. Now, why do I do that? You must have measurements, like I said, with units in the previous chapter. And so I'm going to label a number line with a meter designation here so that I know these members, all these numbers that I see in front of me, excuse me, are in meters. And you will be given the SI units used for that quantity when I teach you a new quantity, such as positions. So positions, SI unit is meters, like this. So you'll see this throughout my videos. A new quantity is defined and then its units are given in SI. Okay, I've got this ball bouncing here. It's going to negative two. It's right on negative two. That means the position of this ball with respect to zero is my reference point is negative two meters. I'm saying right now that zero is my reference point. So negative two meters is the position of this red dot. Positions can be listed with these strange arrows. I'll discuss that a little later. But I can show that this position goes from zero to the negative two spot. So it's that far away in that direction from the reference point. Now, let's look at where this green dot landed on top of the four. Its position would then be four meters with respect to zero. And this would be the arrow that shows how I moved from my reference point to that particular spot at four meters. Then I have here this, that was already in the image, it's two and a half, right here, a 2.5 meter position. And this would be the arrow that shows how I got from the reference point to there. So position is a particular quantity. It seems to have some direction associated with it. And we'll get into that a little later. Now, displacement, very related to position but not equivalent to position. It is the difference in positions of two objects. The final position minus the initial position is how it's defined mathematically. Now, we label that usually with a D or this triangle X. Triangle means change in and it's the Greek letter delta specifically. So some people say delta X to mean change in position. Okay? Change a position has the same units as position itself. Meters, those are the SI units for it. Okay. Now, I'm going to move this red dot from the two and a half positive position to the negative two position. And I'm going to ask you, what is its displacement? Okay? Here's its initial position and here's its final position. Some time later at the end of its motion. And the initial position is the beginning of its motion. Well, I could draw an arrow from where it started to where it ended. Now notice the reference point is not involved right now. Just the initial and final position points themselves. Now, what you do to find position, like we showed earlier, is, I mean, excuse me, what you do to find displacement, like I said earlier, is take the final position, negative two, and subtract the initial position. Okay? Positive two and a half. So negative two centimeters minus 2.5 centimeters gives you a negative 4.5 centimeters. That would be the length of this arrow that shows how I moved from my initial to my final spots. It's negative 4.5 centimeters or 4.5 centimeters long to the left. As you can see, displacements to the left on this horizontal number line will be negative. Okay, let's practice more of these. Okay? I want you to find the displacement of the circle. If the green is the initial and the red is the final position of some object, disregard the 2.5. Okay? So my initial position here is negative two and my final position is five. And this number line, I've given you millimeters. Okay? Sometimes you'll see things where I give you measurements that aren't in SI units. Okay? Well, I'm gonna give you the answer in SI units. Final is five millimeters minus negative two millimeters, which is the same as plus two millimeters. The displacement here is seven millimeters. All right, this next example down here. We start at negative one centimeters. So over here, it's in meters now. Negative one meters and we move to what looks like negative 4.5 meters. So negative 4.5 minus negative one plus one because it's a double negative gives you negative 3.5 meters. So that's the length of this arrow and it's to the left. Notice how in the previous example, positive displacement for movement to the right and negative displacement for movement to the left. If your number line was vertical, positive displacements would be defaulted to movement upwards and negative displacement would be defaulted to movements downwards. Okay? Now, a lot of you are wondering how displacement might relate to another quantity you've used since you were a little child. Distance. Distance and displacement are related but they are not the same and they may not be used interchangeably in physics. Distance, I will define here, is the length of a measurement with only magnitude and so it must be positive and it is not have an arrow associated with it. It has a path length associated with it. The entire path, let's say this ant here, travels this particular path to get from point A to point B. Its distance would be the length of that entire curvy path. It's always positive. I never say I walked negative one miles today or I walked or I jumped negative 15 feet. I was running so fast. We don't say that. We only say positive values. I've grand 15 miles today or I drove my car a quarter of a mile. Never negative distances. The units of distance are also in meters, by the way. So all three of these quantities I've given you all use meters as their SI unit because they are versions of length. So it has no direction but displacement as you can clearly tell has direction as well as magnitude. Displacement can be negative because of that as we previously saw. As you can see with displacement it seems like all I care about is where point A is and where point B is. I don't care about the path I took to get there. Distance does depend on that path because it measures the entire length of that path as a positive integer or real number. But displacement does not. Displacement is independent of the path. So the length of this arrow has nothing to do with the length of this path that we actually traveled and I use only the length of this arrow for the displacement. All right. So now the culmination of all this is to discuss that we have been showing you the difference between normal numbers and what are called vectors. I'm going to look at normal numbers first. Scalers. Here's some examples of scalers. Seven people. 25 meters per second. That's a velocity. 3.6 times 10 to the minus 7 seconds. That's a unit of time. 70,000.12 kilograms. Those are normal, what we call normal numbers. Numbers that we're used to or used to using. They are quantities with positive magnitude only and units. Of course, we've got to have the units. So they're measurements and they're the measurements you're used to using where it just has a magnitude. But there are other units that we've looked at today called vectors. These new quantities we've looked at. Position and displacement. Those are vectors. They're not scalers. Vectors have quantity with both magnitude like we're used to with scalers. So they have a measurement value with them, but they also have a direction associated with them. And of course, units. We've got to have the units. So we've looked at a couple of these vectors. In this particular image, we've looked at d, displacement. So we could say the displacement of this bike was 2.3 meters. You can tell that the bike moved to the right. Absolutely essential for vectors to know the direction as well as the magnitude. The length, excuse me, the angle of the arrow, so its direction in space determines the direction that the quantity acted in. And the length would determine the relative magnitude. So if you have two of the same type of units, two of the same type of measurements like two different displacements, the longer arrow would resemble a larger displacement visually. The smaller arrow would resemble a smaller displacement. This does not work when you have two different types of vectors such as this velocity vector here and this displacement vector here. Velocity and displacement are not the same type of quantity. They have, as you can see, different units. And so they're two vectors. You don't really look at these two lengths and compare them because these units are different. And I've got a bunch of different vectors that you're going to learn throughout this course but not now. So a couple more facts about vectors that I want to show you here. This beautiful bike. It's a nice little Ducati. So the magnitude of your vector is always positive. It's like the scalar portion of your vector. When I ask you for the magnitude of a vector, do not give me something negative. Look at these two velocity vectors here. One is pointing to the right. It's positive 35 meters per second and one is pointing to the left. And it's negative 35 meters per second. Prime, this little prime here. I often use that when we have the same letter for each vector but we're talking about two different ones. I give one of them a little prime so that I denote that that's a different vector. So these two vectors are the same length but they're pointing in opposite directions, hence the negative for one of them. But the magnitude of both of these is the same. 35 positive meters per second. And the length of the arrow, as I've said, is to compare vector magnitudes to each other but they must be the same type of vector, the same units to be compared this way visually. Now there are three different notations for vectors that we use. One would be, and this is easy to use in type format, is a bold letter. And I do that in all the vectors in the previous page and this page. Bold letters to denote a name for the vector. In this case vector v, vector v prime. But you can't do that when you're writing or on a whiteboard. So on a whiteboard you just write the letter for the vector. You don't try and bold face it. What you do is you put an arrow over it. Okay, so you often see that when it's written out. In textbooks you can see either the first one or the third one for vectors or even in your presentations or when you type it out or in a textbook you could see a bold letter and an arrow on top. I really like the arrow notation because it really makes it clear to you that you are dealing with something that has a vector direction and an arrow associated with its quantity. Now we also have specifically, so we don't have to write out the magnitude of v every time we want to find the magnitude of a vector. We can just write one of the symbols for the vector such as the first one here with two arrows on two, excuse me, two lines on other side. Now this is not equivalent to absolute value, but it is somewhat related to the idea of absolute value. The distance from the zero on the number line, it's the length of the vector and it's always positive. Okay, so both of these vectors have a magnitude of positive 35 meters per second. Yes, magnitudes, you will also use the units like you do with scalars. You must do the following when it comes to vectors. You must define which direction is positive. Now since we're dealing with one dimension right now it's either left or right or up or down, but it must be done. This is not arbitrary, you can't just say oh just this is negative just because I feel like it and I feel like this is negative as well. You have to choose one of them to be negative and the other will be positive. Okay, that's what's meant by defining a positive direction so that we can compare directions of quantities. If someone's moving to the left we want to make sure that we denote that differently than someone who's moving to the right so that we can compare those two so that we know they're not moving in the same direction. Alright guys, thanks so much for watching. We're going to get more into this in the next video. Learn some new quantities. For now, this is Falconator signing out.