 Okay. Welcome now to Unit 2 in Physics. Unit 2 deals with linear motion. And our first lesson in Unit 2 is going to be called kinematics. Now kinematics, that's your word for the day today. Kinematics describes the motion of objects or groups of objects. And in this we are going to look at several terms and see how they all relate, what they look like, and how to use them in equations to solve real-world problems. And these terms are as follows. Distance, displacement, speed, velocity, and acceleration. So we are going to see in this lesson how all these terms relate to linear motion, how to use them in equations to solve real-world problems, and we will also check back in with that graphing that we did in the first unit in the introduction of physics. Okay, the first word we're going to look at today is distance. Distance is simply the separation of any two objects. So you got two ladybugs here. Their separation between the two of them is the distance between the two of them. Pretty simple enough. Units can be in the English system. We can use feet. We can use inches. But in physics we typically use the metric and we'll use meters for shorter distances, well really small distances, centimeters, and very large distances, kilometers. Now distance is what we call a scalar quantity. And a scalar quantity simply means a numerical value is given. So how many meters, how many feet, how many centimeters. We also refer to scalar quantities as having only magnitude. That's the word that's used. Magnitude only, numerical value only, no direction. Before we go any further in the lesson, I thought it would be important to talk about frame of reference. In the previous slide, my frame of reference was the different ladybugs. And frame of reference is very important in physics to have a jumping off point. So let's look in the picture here. Figure one and figure two. Just by looking at first figure one, then figure two, you can make an assumption that the car is moving. Well, there's still pictures. Why would you say that? Because the frame of reference of the tree. The tree here, the car is here. In the next picture, the car now has passed the tree. It's on the other side of the tree. So using the tree as a frame of reference, this picture, these two pictures, excuse me, are showing the car has moved. Frame of reference are very important. And we'll use those throughout our discussion of linear motion and physics. Now let's look at the next vocabulary word that we have today. And that is displacement. Displacement and distance are often very similar. And they can be the same thing. But let's really describe it. Displacement is the shortest distance between a starting point. There's your reference point and the endpoint. So let's say here is my starting point. And I take my bike and I travel on this blue path, it's the bike path, to my end. Well, that path that I took is the total distance. What happens if I was able to cut across the neighbor's lawn in the backyard and go directly to where I was going? That direct path is displacement. Well, let's look over here. Let's say I want to take a path from my house to the park. Well, alright, the park. Well, let's put some trees here in the park. Nice little trees, maybe. No, they could be a little prettier. Let's hope there's some flowers in the park too. And we want to go from my house to the park. So the house is the starting point, my reference point. I might follow the bike path. So I might go out. And then maybe the path then meanders around a little bit until I get to the park. That meandering path would be the total distance I went. Now, if I'm able, though, to go directly from my house to the park, that is displacement. That blue line is displacement. Displacement is what we call a vector quantity. Because a vector quantity has not only a numeric value, quantity, there you go, not only a numeric value, but it also has a direction. Displacement is one of those. So if I say that the north is here, and this is south, and this is east over here, and this is west, my and I knew this distance here. Let's say this distance was 100 meters. My direction would be southeast. So 100 meters southeast would be the actual displacement. It has both a magnitude and numerical value and a direction. Well, now we can use these two terms, distance and displacement, and look at how they apply to motion. So our first word here is speed. Now, speed is the distance traveled by a moving object over a period of time. So speed equals distance divided by time. Now, since I'm using distance, speed is also a scalar quantity. It only has a numeric value, only has magnitude, has no direction. So the speed limit sign infinity, oh boy, my husband would love that speed limit of infinity, but just has a numerical value on the speed limit sign, there is no direction. Now, in your moving man simulation from the first lesson, if this was a distance time graph, and your man was moving at a very constant rate, this would be a constant slope, and it would be showing a constant speed here. Constant speed, slope stays the same on a distance time graph. We're going to keep coming back to graphical analysis of motion because a picture really can show what's going on. Just by looking at this distance time graph, you can see that it is a constant speed. Okay, now let's look at velocity. Velocity is very similar to speed, but it also has a direction. So velocity is speed in any given direction. So we'll call that speed with direction. And why I'm using the picture of the cheetah here, because the cheetah is the fastest land animal with speeds up to 75 miles per hour, which is 120 kilometers per hour. Well, if the cheetah is running in this direction, the velocity we could say would be 75 miles per hour east. Just having that direction depicts a velocity. Because we have a direction with velocity, it is a vector quantity like displacement. And vector quantities have a numerical value, which we call a magnitude, as well as a direction, both magnitude and direction. The units for speed and velocity are a distance unit over a time unit, because the velocity equation, average velocity, is displacement divided by time. We also use the same equation for speed, distance over time as well. Many times displacement and distance are the same value numerically as well as velocity and speed. So units have to be a distance unit over a time unit. This would be meters per second. We could have miles per hour. We could have feet per second, kilometers per hour, any distance unit divided by a time unit. And lastly, sometimes you'll hear the talking about instantaneous velocity. Instantaneous velocity is velocity that something has at any one instant. Instance the name instantaneous velocity. So if you are not very lucky and you get stopped for speeding, you are ticketed for your instantaneous velocity, the velocity you were traveling at that instant. Your average velocity is probably well below the speed limit, but you are getting a ticket for instantaneous velocity. Our last key vocabulary word in this unit is acceleration. Acceleration is depicted in all the pictures shown here. And what it is is simply the rate at which velocity changes. So we have the acceleration of this motorcycle, the acceleration of the runners, this one really pulling out ahead, the acceleration of a football player. So acceleration, the rate at which velocity changes. Now to solve for acceleration, we say that acceleration is the change in velocity, delta symbol means change over time. Another way of writing this is that the final velocity, we put a little f meaning final v sub f, final velocity minus the initial velocity over the time will equal the acceleration. And notice that the units then for this are going to be two time units. Because if you have miles per hour and then divided by let's say seconds, miles per hour per second would be an acceleration. In the metric system, we often use meters per second. And then if we're dividing that by seconds, that's meters per second per second. And that equals meters per second squared. There are two time units in the acceleration equation. Now let's look at acceleration back on our graphing that we've referenced in lesson one. This is a velocity time graph. And it's showing as the object is increasing its time, it's increasing its speed. So this shows a positive acceleration. So that's what it's showing. It's showing acceleration in the positive direction. Now what happens if we take that graph, velocity time, and we do this? What does that show? Well, as the time goes up, the speed is, or velocity, excuse me, is staying the same. So this now is showing no acceleration, it's showing a constant velocity. Okay? Well, how do we show acceleration in the negative direction or deceleration? We have time and velocity would be a decreasing slope. As time goes up, the velocity is going down. So this is showing acceleration in the negative direction. That's also what we can call that deceleration. Now if this was a distance time graph, and all of these were depicted in our moving man simulation, this was a distance time graph. And I wanted to show acceleration. I would have to show a changing slope, a parabolic slope, a changing slope, to show that the distance is increasing exponentially, to show the velocity increasing, therefore showing acceleration. Graphing will keep coming back to that. Really can show all types of motion as depicted in this one. Now let's just go and write down that equation once again for acceleration. Acceleration is final velocity minus initial velocity all over time. Now let's see how would we use that in a sample problem. And then I'm going to go through the rest of the kinematic equations after this. So let's say we have a car traveling at 60 miles per hour. So let's draw my car here. I'm such a great artist. And it's traveling at 60 miles per hour. And then it accelerates up to 90 miles per hour. So it's going from 60 miles per hour to 90 miles per hour. And it's doing this in let's say, oh, three seconds. So it's doing that in three seconds. Well, how would we find the acceleration? What is it? Well, the initial 60 miles per hour is VI. The final 90 miles per hour is VF. And three seconds is the time. And so we can just simply look at our equation and plug in the values. We have the final velocity, which is 90 minus the initial velocity, which is 60, all over the time, which is three. So 90 minus 60 is 30 divided by three. And the answer is 10. But that's the numeric answer. What is the units? Well, I should have probably been keep carrying my units. But the top we have miles per hour at the bottom we have seconds. So that would be miles per hour per second, 10 miles per hour per second. Now we'd like to highlight the three main equations for kinematics that we have. The first one really is just a rewrite of the one we just did. Acceleration equals final velocity minus initial velocity all over time. In physics, we like to write equations whenever possible as linearly as possible. So if I cross multiply, I would get VF minus VI equals AT. So I cross multiply across the equal sign and put VF equals VI plus AT minus VI plus AT. And another thing physics equations don't like whenever possible, they don't like any negative signs around. So I am going to add VI on this side and my first main kinematic equation is VF equals VI plus AT. So that is, I call that number one, the first key kinematic equation. Final velocity equals initial velocity plus acceleration times time. And we will use these in lots of problems practice coming up. Now our second kinematic equation does not have the final velocity in them. The kinematic equations are devised so that you can use one of these equations to solve them as any problem dealing with linear motion. Well, let's derive this one. Now you do not have to know the derivation of these equations. I like to show you where they come from, but you don't have to know how they were derived. But it is interesting to see where they come from. If I wanted to find the average velocity between a final velocity and initial velocity, what would I do? Well, you add them up and divide by two, that gets you your average. So since we know that average velocity is distance over time or displacement over time, and the average velocity here, and I'm going to write this as D equals velocity times time, average velocity times time. So I'm going to rewrite this as D equals VF plus VI all over 2 times T. Now if we want to get rid of the final velocity, the only reason we want to do that is that we might have problems where the final velocity is not given, and we want to find something else. So if we want to get rid of that, I'm going to substitute my first equation in for VF because my first equation was VF equals VI plus AT. I'm going to substitute it and I'll do it up here. So we'll have D equals. So instead of VF here, I'm going to put VI plus AT, and then I still have that other VI, all over 2 times T. Okay, so let's see if we can kind of make this look a little prettier. So we're going to add the two VI, so that's two VI plus AT. And to make it easier, why don't we already multiply through the T? So two VI T plus AT squared all over 2. Okay, now it's just a matter of a little cleanup here. So our final kinematics equation, I'm going to cancel out the two here, and I have VI T plus 1 half AT squared. And that is our second main kinematic equation. I'll call that number two. Distance equals initial velocity times time plus 1 half A, which is acceleration T squared. Okay, let's on to deriving our third kinematics equation. Well, all the equations thus far have had time in it. So let's see if we can get an equation together that doesn't have time in it. Okay, so I'm going to start with my D equals my average velocity, VF plus VI all over 2 times T. I'm going to start with that one. Okay, and what I'm going to do in this equation is get rid of the time in there. Well, how am I getting rid of the time? I'm going to solve the first equation, the VF equals VI plus AT for T. If I do that, T equals VF minus VI all over A. So that is the first equation solved for T. And I'm going to put this in for that. Yeah, it might get a little messy. It's okay. It's kind of fun. So we have VF plus VI all over 2 times VF minus VI all over A. Well, let's try to get this linearly as much as we can. So I'm going to multiply both sides by 2A. So we're going to have 2AD equals, and now I'm going to combine these with the FOIL method. You probably remember the FOIL method from algebra. FOIL first, then O is outer, I inner, L is last. So let's do that. So VF times VF, that would be VF squared. And then we have this, the outer, so minus VF VI, multiply those together, that's a VI. And then we have plus VF VI in the middle there. And this would be minus VI squared at the end. So that was my FOIL. VF squared and then minus VI VF plus VI VF and then minus VI squared. Well, what's nice about this is these just nice cancel out because one's negative one's positive. And now we're going to clean up again. So what I'm going to do, and I'm also going to do it on the correct side, is I'm going to bring the VI squared over here and then I'm going to just flip it a little bit so that it's left to right. So our final equation is VF squared equals VI squared plus 2AD. That's our final kinematic equation. Number three, let me go over that one more time. Find a velocity squared equals initial velocity squared. See, I got rid of the negative sign because I had brought it over. Plus two times acceleration times distance. Well, before I end the lesson, let's go back to our good old falling calcime here. And the reason I'm showing this again is because anytime our problems have objects that are in free fall, we already know the acceleration. Acceleration is known, oops, there we go, that's spelled correctly here, when you're in free fall. And that is the value for the acceleration of gravity. So that is a known quantity. So we call that G, anytime you're in free fall, you already know the value for G. And that equals 9.8 meters per second squared. And we'll use this a lot. Okay. And oftentimes we'll use it as a negative 9.8 meters per second squared because it is a vector quantity, acceleration is a vector quantity. It has a direction. I did not state it earlier, and I'm sorry, acceleration, vector quantity has a direction. In the case of gravity, it's always down, right? When you drop a pen, you don't think, hmm, I wonder if it's going to go up. No, it's always going to go down. So we already know that that is downward, acceleration of gravity. And that is a known quantity. So as long as the air resistance is not an issue in the problem, the value for A is known. And that'll help us out a lot with our kinematics equations because if it's in free fall, we know that value for A already. Our next lesson, I will be doing a practice with exercises for you to go through problems, try some of your own, and I'll go through step by step how to use all these kinematic equations in problems.