 She's on video and she's got a note taker. She's figuring. I'm not getting down a bed John Tyler first Bill Samantha Andrew Leesh my Leesh you guys can all look that up from a Robin Hood movie see what that way it means Joe Bill Patrick Mike when's cast come off? Yeah, okay, well other party mark Tyler seconds not here Tyler first is here, but not Tyler second Al and Andrew quick word about yesterday's lab easy as it was and it looked like most everybody got good results What happens sometimes in those type of things is is People get the X and the Y axes Remorse if you do what happens to the reported slope You'd what? Yeah, you get one over now Now you can check to make sure it was still right, but then you got to think you know my reader Isn't going to want to make that step my reader my boss is not going to want to fix that step that I screwed up So I've got to reverse those and make the slope pie that we are looking for You you need to look for things like that. It's very important What's on the x-axis? What's on the y-axis in terms of what's going to be recorded as the slope? Now I hope most of you've had a chance to look at that thing about graphing and Are starting to get the idea of what we mean about chart junk That that shouldn't even be a new term anymore as of yesterday Not a term I coin, but I think it's a superb term. It's any ink. That's on a graphic That doesn't enhance the information What often happens and if you ever look at USA today newspaper and the graphs they have there They always have something at the bottom of the page illustrating the the national debt or or Car crashes due to texting or something whatever their topic of the day is and they've got they've got little stars on it They've got colors all over it and they've got airplanes here And they've got bubbles and faces and cartoons and it's all chart junk because that doesn't enhance the information It enhances the entertainment and that's not the business. We're in business of information in here Entertainment's great. It's not on company time Then you shouldn't sit there. You should sit there No, no, you'll find out very quickly I care less when you come Pay to be here if you don't want to be that's your business. I'm we your check is clear But I appreciate that. However, there's the best way to handle it right by the door time comes Slip out back. You can slip out when I'm doing this and I'll turn back and I'll think I'm going crazy Because that's one of my one of my dominating feelings at this age anyway Alan sit on your head Not yet I don't care. I'm not the point here again again the information is the point Appreciate that it is hard to be a rock star. Nobody knows how cool. I love that. There you go so actually what I'm more worried about is and I don't know about bill And the rest of you it's not a worry yet Samantha don't worry. It's called male pattern baldness That I'm worried about when I'm on camera. You can worry about that later. I don't bill I've never seen your head because in the second class. I've ever had you've never not had a hat on you. I don't know Yeah, you oh, yeah, yeah, so you don't want to come up That's the way things and he never goes anywhere Yeah till you die All right, so what we're what we're concerned with is that chart jump stuff that doesn't enhance the Quality of the information and it's portrayal Doesn't belong there. We have a single line graph So most of you notice when we put up the data points and then when we put up the trend line We now had a two two items in the legend Well neither one of them are in any way useful. So kill the legend Kill the grid lines. We don't need the grid lines there Some graphs you do because you'd expect the reader to actually pull values off the grass You want to use the line pull the graph values off the grid lines could be important to make sure that they travel over horizontally when they need to Why Excel thinks of default of horizontal grids and no vertical grids. I don't know God knows what's going on in the Excel office up there because there's not a brain in that Organization that actually works with graphics Because they wouldn't and that it comes up with that gray background too That's definitely chart jump. That's ink that doesn't in any way enhance that the information So you need to clean a lot of stuff up on these graphics another thing that'll happen for some of you is Is when the numbers come up here? Maybe it's something like forty point zero zero twenty point zero zero Ten Guess that would make sense. It's even the space of thirty that point zero zero is useless It doesn't enhance the graphic at all. It just takes up ink takes up space It just get rid of that stuff clean things up Every little piece that you can take off of that plot Leaves more prominent your results and you want your boss to flip that page over and go bang There it is exactly what I was hoping we'd see Excellent work Call you up Showed you how long ago. I was a nice job. You can we'll let you back into the company picnic So You don't want to turn it in yet. I bet there's still some cleaning up. Oh, yeah, I was just trying to find the drop box So it was done. Okay never Are we going to have any graphics and I can't imagine why anybody ever would that along with the numbers There's not a title for what's going on on that axis. What are those numbers in our case? It was the the diameter of the object With units, I think most of you caught that anyway Also Same thing here. Make sure that it reads Sideways you have the option of making it read like it's on the outside of a movie theater or something Where the letters are going down like that. That's a very very difficult to read If you ever have any doubts if something's readable or not readable hand it to one of your buddies say look at this You've got three seconds to give me your impression Because you should be able to start digesting the plot that quickly and if you say You can see him struggling to read something fix it Use each other you know here you proofread my thing all proofread yours Get little proofreading circles. You can have proofreading reading potluck dinners internationally themed proofreading potluck dinners at each other's houses as you rotate How fun would that be? All right, so there's lots of cleaning up to do Yeah What we had circumference here don't do it don't do it like that very difficult to read do it Like also, I think with several of you actually Demonstrated how a simple graphic like that doesn't look good big. It looks much better smaller Who'd I do that with actually did it on their screen with them did with you land what it was? It was very true. We took two copies of the same thing made one big one one small and The small one was very much more readable. So don't make it big. It's not going to help anything Lastly before we get into the work Data table anybody put one in their report so far good. Do you think I want to read data? Yes, do you want to read data? No, I want results Not data. That is what you needed to get the results and The results sometime could appear best in a data in a table Then it'd be a results table not a data table, but those Individuals details that you accumulated yesterday. I don't care about You need to keep that kind of thing on record Because it could be that we get this beautiful result and somebody says I don't believe it make it prove it And we go trade some down and this will be my boss It will come down to your office and say you got approved this you'll pull out then your data table and say see here Says right there poker chip quarter basketball And we'll say yeah, okay We apologize because bosses are always very willing to apologize But I don't want to read I don't read your dad. That's why a lot of you asked What should I call this you were holding it and say what do I call this and I kept what did I say? So I don't care all that anything you want because I'm not going to see it Yeah, ring type thing. That's what you had a moment. All right, so any other questions? Inclusion do you want to also include all the questions or do you want that separately? Were there questions in there? just a whole bunch of Yeah, yeah, yeah, that should be in there just because this is one of the times when we Know for sure whether our results are good or not So you have to say whether they're good or not by how much? If you do that equation as written to it'll you come up with a plus or a minus if you were underneath You're below by a certain percentage and that'll be reflected because that could be important too But yeah, that that should be stated as part of the result because none of these results mean anything If we don't have some idea that we can put confidence in your and if you've got to pie within 0.7% Pretty confident right There is on angel an area for discussion questions You got a question as you're sitting down to write this let's see it's gonna be due Tuesday, so a lot of you'll start it Tuesday breakfast That'll be a little late, but if you're a lot of you have already written a bunch of I saw Several of you got at least halfway through a start But if you come up with a question put it in there That way I only have to answer things once not not six times plus everybody gets the same information So it's a lot more fair So use angel Some professors actually run their classes through Facebook We we've got angel we paid for it All your other classes are there whether your other professors use it or not is their business So we'll use it. We'll make use of it. All right. Any other questions on that before we go on? All right We'll be out of here at 20 after I promise You got so much extra for your dollar yesterday. All right Well, we work on as we went over time on Monday. We have so dang much fun. We just kept going Well, we're working on yeah flip your notes back to see what we finished up Phil Yes, we were converting units. It's an absolutely vital skill You've got to be able to do it. You've got to be able to do it correctly And you've got to be able to do it in such a way that your boss is confident. You're doing it Well, it's a terribly embarrassing thing. I hear To go before your boss with some numbers And your boss says wait a second What are your units here? Terribly embarrassing thing here You go slumping on it. Oh, that's a long walk back to your office to go fix that stuff That you should have caught in your freshman year with your great physics professor All right, so we're gonna we're gonna do another converting units thing. However, remember There were two things You needed to remember to convert units What was one of them? What was one what was one of them? What was one of them? No, what was you can multiply by one when you multiply by one? Nothing changes. Well the quality of the thing changes because we're trying to change centimeters to meters or hours to lifetimes Whatever it might be the quality of it will change the quantity of it will change but the quality won't it's still Length units to length units time units to time units, etc. Nothing else can happen when converting units So we'll multiply by one and we'll do it as many times as we need to Which we didn't hit on Monday We did it once but we can multiply by one as many times as we need to until we're done What was the second thing we had to remember? That not that you had to remember but just the it was one of those things that was just so obvious I needed to bring it to the four Mike You're gonna start with Something that's a equals a but that's what's going to give you the one that you need to multiply by because if a equals a then A over a equals one and that's how you pick the one in it that you want to multiply by Because there's a million ones out there to multiply by Some aren't any good and you don't want to waste your time with them. You got to get the right one and It's not very hard as we'll see here shortly. So we're gonna we're gonna do another unit conversion I Want everybody's familiar with 60 miles per hour the speed all you guys use going down Bay Road the speed I use on the north lane 60 miles per hour I want to convert it to so I'll leave myself a little bit of space I Want to compete it convert it to? let's say Feet per second remember I said that was our those were our basic units in the English system for length and time feet and Seconds so we want to make that conversion for what we do is we multiply By one we just have to pick the right one to do the multiplying bit with and we'll be all done and This if you do it this way you never have to remember doing multiply do I divide? It happens a lot with the SI prefixes killer and milling you forget do I multiply by divide? I don't know what to do You don't need to this will tell you what to do anybody offhand Know the conversion where so many miles per hour equals a Certain number of feet per second anybody know it offhand Who would guess it would have been Alan? You is everybody getting to see there'll be a slow migration of people as they come and sit in class Until there's just this vacuum around Alan and all the weird stuff. He knows Alan are you are you a hundred percent sure you know it? That's not what I ask Alan you have Alan Answer my questions when I ask them otherwise we start going in six different directions I ask a question. I want that question answered You know I'll bet all right What do I put in here? How many feet per second in one mile per hour? No No, no, I asked for the number you started to give me two numbers Do you know Andrew or you scared to answer now? No, what are you looking at put that away? Nobody here Either will admit to it because I'll jump all over them or Don't I don't know I don't know how many miles per hour equals how many feet per second if I'm driving one mile per hour How many feet do I cover in one second at that very same speed? I don't know what that number is I Don't carry useless information around in my head Great is that the same thing as a foot per second? No, it's not so keep it to yourself Alan Unless it's useful You're you're you're you're charred junk Look if don't think for a second if I murder a student on camera, I'm not gonna edit that out Evidence will be gone So So we need to do something else and that's what Alan was trying to drag us to by not answering my question We're not going to be able to do this in one step because we don't know what this a equals a thing is to start with So we're going to have to do it in a couple steps Maybe two maybe more we'll do as many as it takes Can we go from miles? To feet and get partway there do we know one mile? equals How many feet? Alan does I does because I was born in Denver, Colorado the mile-high city and if you go to the Capitol building There it is right on the front step One mile above sea level Says so many feet. You're all Americans. You should know this number anyway, and it's 5,200 and 80 So there's our first a equals a That will give us our first one to multiply with What we have to figure out is what a goes over what a? Well, we'll let the numbers tell us I have miles up here The only way to get rid of miles up here is to have miles down here. So take my a equals a Just fill it in and I'm already a little bit closer now. I have feet per hour Driving 60 miles per hour How many feet are you going to go in that hour? Here's the number to tell us. We just have to multiply that out No guesswork You didn't even have to guess that because you just asked to keep Alan you might want to get Alan's Cell phone number Because if you need something useless, there's a man. It's going to have it at his fingertips In here darn well, but I could have it on silent vibrate All right, so we're a little bit closer. We've already got feet on the top feet on the top All of this remembers we're just looking at the units. I don't care what the numbers are and as long as I've got them right They're all going to take care of themselves Now can I get hours? To seconds Some of you might have it in your hand directly some of you might not doesn't matter if you don't have it directly We can put it together An hour is let's take the next step towards seconds. Let's do minutes. How many minutes in an hour? Sixty most everybody knows that you wouldn't even have to go to Alan for that one We just need to figure out what goes on the top what goes on the bottom hours on the bottom We'll be cancelled with hours on the top. So just fill this in Those two things are equal. So I just multiplied by one hours, cancels hours We now have feet per minute. So the last step we need to take is to get to minutes to seconds and You don't even need to worry. Dang do I multiply do I divide I always forget I Always forget too because I know I can just do this and fix it. So I don't bother remembering Minutes on the bottom Minutes on the top seconds on the bottom. We're all done Now you do exactly what the numbers tell you to do and you've got it perfectly converted 60 times 52 a divided by 60 divided by 60 you can't screw up here It's the it's the foolproof unit conversion The reason I Be kind of laborious about this is because one I Could never figure out the first person to show me unit conversion with my high school chemistry professor And he'd love to make it look like it was some magical thing. Oh, I just do this and this and this and this and this and we're all How do you how do you know do that and that now I couldn't be I Took me years to finally figure out. No, I got what he's doing. It's this simple I don't want you to think this is magic. It isn't This is this is a this is the engineering equivalent of tying your shoes. You've got to know how to do this Or you're gonna at the least look like a fool in front of your boss boss at the worst You're gonna be brought up in criminal charges for being negligent negligent in the design of a product that killed people maybe thousands Stuff goes wrong all the time in engineering. It puts a lot of people in jeopardy Sometimes it's as simple as this. I don't want that. I don't want to see your name in the news for this kind of stuff winning the lottery where you thank your College physics professor in your statements where you collect a check that I want to see Your name on the police for the engineering police plotter. I don't want to see your name there Who's got this number for me then? 60 times 52 80 divided by 60 divided by 60 88 feet per second sometimes Since it's one of those very very common numbers might be FPS Though that makes unit conversion a little bit harder when it's written that way so We won't bother with that, but we'll recognize it if we see it now If this conversion ever comes up again You can shortcut all of this with a new a equals a you can say 60 miles per hour per second you've got a now a new a equals a and you don't have to go through all of the steps anymore You can even clean it up if you want and divide through by 88 so it's one Feet per second equals whatever that is three quarters of it if you want to clean it up a little bit You can write that in your book. Remember the tests or open book open notes You can write that in the cover of your book. You don't have to make the full conversion anymore Any a equals a will work as long as it's the right one in the back of your book Oh my gosh, this is my book and I have this page tagged because it's that important Nothing but pages of a equals a's All here for you. We're working with speed So we look down here. Oh We can give her angle length time mass area volume Density speed. Hey, there we go speed We were talking about miles per hour. So I look in here somewhere. There's miles per hour equals 1.467 feet per second That's this thing right here divided through by 60 It's already done for it energy power pressure acceleration force Some of the favorite words in our life from here on out They're all here and there's there's something there's something there's a hundred in here will never even use But they're here So tag that page for exams It can save you not just ten minutes, but under pressure again, you could screw that up and not catch it Now you don't you know, you get it just right pages of a blade right there for you As my gift to you All right, a lot of the homework problems Practices this is a lot of what you need to do in this first homework set a lot of these unit conversions so Baby sit the units watch them write this cleanly and carefully That's the main way students grew up is they're just lazy with those stuff Don't write it cleanly. Don't write it carefully. Don't cancel the right things at the right time A big trap and I think I talked about it was when we have units that are squared Did we do that? Yeah, you have to square the a over a the whole thing not just the units But the number that goes with it also gets squared So be careful with that practice it And get this kind of stuff down right so your boss has confidence Samantha God bless you look at she's already tagged That's why she's my favorite Okay All right, I'm gonna go to more stuff. Let's get into the physics now More of this. See how nicely it erases because I've preconditioned the board. That's beautiful All right, we're gonna we're gonna open our work here on the real physics That that was that was all kind of background stuff. We needed to get going We're gonna work here to start with and what's called kinematics specifically We're gonna start with rectilinear Kinematics most likely to do most of you a new word So let me see if I can come up with a Clearer way to say that D one dimensional motion That's rectilinear kinematics One D motion in the most simple terms We're gonna be talking about some things moving and in the way they move But they can only move either left or right but not both It's a train on a very straight track Just to get us started. There's there's there's a lot of good physics that goes on in here But it's also not very complex physics. So it's a really good place for us to get started So we're gonna start with that will very quickly be into 2D motion Which is called curvilinear. That's where things can go left or right and Up or down at the same time and any mixtures thereof just the very same thing you do Every day on the surface of the earth for the most part. Yeah, it's curved It's really a three-dimensional space, but not locally to us. It isn't we live in a flat world locally We know the earth is spherical but My building isn't so we'll get to that. We'll do a little tiny bit of 3d motion. We won't do a lot Because It's the same as 2d motion for the most part except there's another dimension added on We won't do much with it also because it's very difficult to draw. It's difficult to take notes for it It's difficult for me to draw the board. It's difficult Some people have a lot of trouble even conceptualizing three-dimensional images on a 2d surface Think of the generations to come who won't even understand what a two-dimensional movie is that all everything's 3d Good morning America on television Kathy B. Gifford in three dimensions In life get any better. All right, so we're gonna we're gonna start with this Kinematics in specifics is nothing more than the motion itself. So what we have to start with two things To get started with this that there's there's four parts really this far as we're concerned with kinematics We need just two of them to get going and then the other two will come very quickly to us The first thing we need is the concept of time that as we're talking about objects moving in whatever fashion We need to know when they're somewhere that we're talking about well There's the other thing we need is position We need to know where something is and when it's there or we can't even get started on kinematics So those are the two things we're gonna start with when something is where it is All right times easy enough Because we can do that with a stop watch. We'll talk about seconds to represent time maybe minutes We do some planetary problems So maybe it makes sense to talk about hours or days or years even even centuries to come into some of this but It's you all got it and you know how to get it You look at your watch. By the way, this is a watch. A lot of you don't even know what these are anymore or you plot your your cell phone most of them have a stopwatch Function in them stopwatch tool and if you want to use that over in lab when we're timing something great Works fine So that's not a big deal, but we will give it a variable letter T Just just to show how creative America Alan you have that function. You need go get a new phone Man see you cheapskate All right position Well, we got to give it some we got to give it some variable letter to Maybe if we're talking about right motion and left motion X will work Because you're pretty used to that Maybe if we're talking about up and down motion only we should use why because you're pretty used to that But it doesn't need to be Doesn't matter what we call it. We can be as generic or specific as we want with it. So just to put something down I'll say s That's general if you want to use X when we're talking about horizontal motion. No sweat. I know what it means I'll catch it when I use Y for up and down In lab next week. We're just going to do some up and down motion only and it may make sense to do why because we're used to it No trouble. No trouble. All right. So so time no big deal that we have to worry about But position that takes a little bit more definition Position has got to be measured from somewhere Yeah, if you're going to tell me you're two miles away I got to know two miles away. What from where if you don't tell me the two miles is meaningless Yeah, you've got a number there to I understand the units I understand But I don't know where to measure it from so it's no help whatsoever So the very first thing we need to get started here Is we need an origin of some kind just a place from where we measure things Must that origin be anybody have any idea where that origin should be? What should we call the origin? I know that you're all of about the right age to think still think that you're the center of the universe And I know your mommy thinks you are Or the center of her universe But I don't know if that's going to go so well in a math Physics class with a whole bunch of centers of the universe So where should the origin be that we're talking about? Anybody want to take a guess John? wherever you don't want to say it's got to be Omaha, Nebraska the corner of fourth and main Because that might not be useful to our problem. It certainly wouldn't be to our useful to our problem out here in Queensbury Let's put it somewhere useful So there's the first place For helping us choose where it's going to be. Let's put it somewhere useful Somewhere close to the problem. Otherwise the numbers are going to be huge and hard to measure Mike got something else to add to it We could But we don't need to what's easier to do is to say when the object is at these Origin we'll call that time equals zero actually we're going to pretty much get rid of time equals zero in a second Anyway, but we can say whenever we want is time equals zero because what we're most concerned with is not The time itself because again that has an origin. What are we going to say the creation of the universe? Which for some of you may be your belief that it was 6,000 years ago Others of you may think it was 13 billion years ago. We're not in the class here to argue over that one But we want the origin of the time to be local to so we can say t equals zero quick That's all we do with starting the watch Time equals zero we started So that's that's got an origin to it itself. And yeah, we want a useful one of that as well Another quality of the origin That's absolutely vital Actually, we that doesn't need to be vital. It doesn't have to be useful, but boy, it sure helps But what what is something that's vital for the origin in a problem? Alan are you dying to say something and you just won't? You can say something if it answers that question Measurable I mean how big it is how big Why open on the grass if you want to somewhere nearby that's what useful means local Fixed yeah, you don't want the origin wandering around You know we started measuring one thing and while we're concentrating on where it is and when it's there our Origins drifting around can you imagine trying to measure something with a tape measure? You're off here one end measuring and the jerk on the other end is walking all over and we try to measure something with a Little brother or sister. I bet that's exactly what they did butterflies to chase And dogs to pet and all kinds of stuff going on there goes your origin all over the place It sure helps if it's fixed just so our When we do make a measurement the measurement in regards to our origin and the information we're sharing Is is static non-changing we don't want the values to change be like a Harry Potter world of physics You know we're all the pictures on the wall are always moving Be like that all the dad on our page would always be moving terrible What else is real important? With the origin well It's got to be it's crucial that I know where your origin is If you're giving me information with respect to that origin if you tell me information of An object that is a certain place at a certain time, and I don't know I can't hang that on there And you say it's two miles away And we're on the phone, and I don't even know where you are act that doesn't help me any it's got to be information We share We don't have to necessarily have the same origin Certainly if we're doing two different problems or you're doing a problem on your paper and some else doing yours You'll each have your own origin, but if you swapped pages And it's marked on your page. You know where it is. He's talking about It's information that's shared So let's say the the origin let's let's put this Let's just say the origin is known. It's not a secret where the origin is Whether it's a dot on your page with an O beside it that works Whether there's a signpost there saying here in lies the origin of all things true and strong Which of course be right in Denver, Colorado where I was born That's not only the center of the universe. That's the center of all the known universe Mike is that a hand up a broken hand up? One other thing and I'm not going to belabor the point to try to make you guess this one because it's not going to come up But it's a very important thing ties all these other things together It's arbitrary where it is You're doing the same problem on your own paper You put the origin over on the left. You put it over on the right. It doesn't matter Because you're going to make it known you're going to leave it there and Either way, it's useful right down the page. So it's arbitrary That sort of ties all of these together Anyway, you get to make the choice of where the origin is when I'm doing problems at the board I'll either choose it or we'll choose it together But I'm just going to put it there somewhere let you know where it is and off we go with the rest of the problem So to start with We're doing straight line motion There's a straight line. So we'll move along that straight line Could do it up and down, but I'll do it that way No reason not to if you want to do it up and down in your paper. Nothing's going to change. There's the origin Is that an o or a zero because we need both if if an object is at the origin its position s is Zero so it's going to serve as a zero and oh That's the that's the poetry of the universe right there That tells you God speaks English that he made zero and oh have the same shape All right, so there's there's oh, maybe our object is there at t equals zero Maybe it isn't it doesn't really matter It depends upon the problem Some problems start at the origin some problems start at t equals zero some don't It doesn't matter because what we're most concerned with is Not the individual time and the individual positions But how those things change because that's where things are more interesting That's what we need to do as engineers and scientists. We need to study how things are changing Well, how do we make things go from here to over there? How do we bring them back? Something's just going to stay where it is be a single point. You don't need engineers You can go get any you can go get the business majors and they can run the world So easy that is We're engineers. We run the world So it We're interested in the things changing so let's do this Let's put our object there We'll call that s one for position one It's there at t one So you're already getting an idea of this this nomenclature we can use we can put a little Subscripts on there to tell us when things are where they are Notice that the two subscripts match each other It's here at that time and that t one and that s one go together We could use a different system where those don't match But you're just going to screw up somewhere else when you do something like that So make sure these things match that the things that go together go together and We'll be all right. Let's see We need units So we'll call this meters just start throwing some numbers on here We use nice round numbers to start with let's say this is three meters and We'll start our clock there. So S one equals three meters T one Equals zero seconds and our our problem begins some amount of time later what Mike? It's not there No, you you said that I said maybe no somebody said who said that wasn't you yeah, I said maybe But I said maybe not it depends if if our object happens to be here When we're interested in starting the problem then let's start to watch there Remember the origin is arbitrary So just makes a little more sense to me because that's the first place where I have the object That that's where we'll start the time because maybe it took 15 years Three months and 27 days to get from there to there. Do we want it back to reflect that? Not not for what we're doing here because the problem only just started So let's start to watch it. That's us. We know where the object is We'll start the clock there Three meters. Oh, that's manageable if it was three light years I'm all I'm change where the origin is and redo the problem from there But again the origin is arbitrary, but it's a place useful. It's useful to start the clock Right there. That's one All right some amount of time later and again just to keep things simple. We're working whole numbers. It's here that looks like S2 is About what that looked like about five meters just using some round numbers keep things simple and Let's say it only took one second to get there something a little bit more interesting going on because now Stuff's changing we can start to wonder why did it change? Is this a design problem I need to do I need to make sure it gets there in one second or my design won't work Do I need to prevent it from going there or my design will work all kinds of now? No, we got stuff to do So we although we can even ask ourselves now It was there at zero seconds a second later. It was now down there That means it was moving at least some time during that We can ask ourselves something simple like well, how fast was it moving? Let's see. We'll call that V for velocity We're a little bit. We're a little bit constrained in that we only knew where it was here and Here we don't know what it did in between So we're not going to be able to say a whole lot about how fast it was moving Because we don't know what it was doing in between Maybe it went down there 300 meters in the first half a second came Zipping back here and then finally ended up here a second later, and that's the only time we woke up to check it So we can't say in a lot of detail how fast it was moving, but we can say On average how fast it was moving and we do that in exactly the same way you would do it as We talked about even on Monday if it takes three hours to drive to New York City and It's a hundred and fifty miles to New York City. What was your average speed? Fifty miles per hour You know, you all know how to do that Distance traveled Divided by the time taken were you always going 50? Now a heck no because between here in the north way You went 30 You wanted to go faster, but there's cops out there Then when you got on the north way 85 Tell you hit the first Starbucks I pull in there get a venti cream Lada a doobie Pacino What do you do with Phone and all that stuff's incorporated in that story But we miss all the detail because we're looking only at two points With nothing else in between I don't want to write that every time one thing engineers inside this are famous for is being fantastically lazy So we're not going to write out this stuff if we can do something shorter So we're going to say let's see the time the distance traveled Well, that's where it is now minus where it was then and I have to do it that way it has to be two minus one it has to be the later minus the earlier We'll see specifically why in a second as we illustrate this And I want the same time interval That goes with that so if I did s2 minus s1 I got to do t2 minus t1 Let's see. What's that come out to be? s2 was five meters minus s1 which was three meters Notice that I'm even too lazy to write the meters on both of those numbers But we all know I could never subtract something that wasn't meters from something that is meters So if I put meters to follow everybody knows those are both meters and T2 was one second t1 was zero seconds I'll do the math in my head for you average speed two meters per second Simple as that You know what I'm too lazy to write this so I'm going to write Delta s over Delta t Universally understood notation and probably you familiar with it anybody never seen that before I'd be very surprised. It's Very very calm just means change in Change in position divided by the change in time Later minus earlier later minus earlier always that way Simple as that so We we go away for another coffee break. Oh, no, we already had a coffee break So now we have to take a bathroom break and we come back a second later Well, Samantha's going nobody's gone to the bathroom in one second Man, there's always a line out the woman's bathroom. That's 23 people long No way you can do it boys guys. We're all thinking one second. What were you doing for all the rest of time? So some time later My golly if it isn't here here's s3 at time t3 So we'll we'll give some reading that looks like we'll call this Well, I can't call it two meters Because in here is two meters So I'm going to call minus two meters Because I have to make it clear Exactly where it is to the left of the origin. We'll call that minus you're used to doing that type of thing that's not new I hope and It took another second to go there Sorry, we're at one second. We'll call this two seconds These time steps don't have to be even sized It's just whenever we happen to be able to take a reading now What was the average? Velocity says to three time step to time step three What was the average velocity? Delta s over Delta t. I want Times that two to three It's always the later one minus there earlier one three minus two They always have to match above and below Three minus two Otherwise you're gonna have a time in a position that don't go together in the problem Screw all kinds of stuff up Let's see at s3 It was at minus two Minus where it was at s2 that means minus five watch the minus signs of Anything there's two things that can drag a really good student down as easy as anything First thing is screwing up the units You don't watch the units You're gonna screw up second thing is not watching your minus signs They're as important as anything else that we do That minus sign Absolutely crucial to get in this simple simple problem correct and T3 was two seconds t2 was one second Seven divided by two. I don't like fractions. We're engineers. We go to decimals minus 3.5 we'll call it minus 3.5 meters per second They do that right. I didn't do it. Oh, no, it's divided by one I'm getting so excited here. I'm just having so much fun. There we go minus seven. We didn't have a fraction. That's it We have a fraction. Yes, Allen It's not going up at all this is one of the motion it can't go up That's what I'm saying Because what it did here is Very different than what it did here here. It was moving right on average Here it was moving left on average if we don't have the minus sign to tell us that How are we going to know it moved this way seven meters or went seven meters per second farther? We wouldn't know we'd have no idea This minus sign tells us an awful lot of information that we need to know It also implies direction So that's the difference then and you asked me this the other day Allen that's the difference between velocity and Speed speed everybody's familiar with you tell me yeah mom and earth way I say yeah, what's your speed? You look down to your speedometer your speedometer And you say now I'm going 85 miles per hour Actually, you'd say I'm going 85 Because that way you know if you're really only go along 30 and you don't want your pals to think you're a no Grandfather you keep the units off So sometimes it's useful to leave the unit top But but you're on you run the phone you say you're on the north way going 85 is that going to be answer going to be different Whether you're going north or south No matter which way you're going you're just going to say I'm going 85 The speedometer on your car only says 85 whether you're going north or south or you're on the mass pike Going east or west or going down to Binghamton diagonally on a 88 Five bucks anybody knows This is the north way That's the through way 88 is The what way is not the wrong way and to pay out this five bucks No, it's the quick way You know that well no, of course you didn't you'd be five bucks richer if you did it. It's the quick way Anyway, your car will need read nothing but 85 Plus eighty four well it's implied plus. There's no plus on there. It only reads 85. That's speed Speed is simply How do I put it? I'll put it this way The magnitude of your travel there'll be units in there, too It's a 85 well we know it's miles per hour because you're in the car and that's what our American cars read Nothing better on the road than a GM vehicle Velocity is different velocity also has in it Direction and that's why I used a v here and not an s I wouldn't want to use an s because I already used s for position But I didn't have to use that s for position. I could have saved it for speed But speed doesn't have enough information. I need v for a velocity. So this is magnitude direction That's velocity and that's what we're going to be most concerned with is Velocity more than speed but Be careful when we use those terms because now there's a difference before there was never a difference When you go back out in your car, there won't be any difference You talk to the poor smucks on the street who don't know this kind of stuff You got to talk to them the words they understand you can have your simple words like speed But they know what you're talking about Actually, you talk to them out there. You use the word velocity. They don't know the difference There is a difference and it's that simple component of direction Because we're talking about an established origin In a particular direction So that minus sign is absolutely that minus sign is as important as the seven is in terms of the information it conveys to us All right, another quick question here. What was the average velocity? From Time one to time three we did time one to two we did time two to three It's Delta s over Delta t. It's always that for average velocity What should I put s? What minus s what the later minus the earlier? s3 minus s1 T3 minus t1 they got a match Hey, wait, wait, wait. What happens to time two? We don't care. That's not what I asked. I asked what did you do between one and three time two doesn't come into it That's the meaning of average velocity. We only take the two end points We ignore everything else in between no matter what happened So we just fill this out from our amazing chart s3 is minus two minus from the equation s1 Which is three t3 is two Minus t1 which is zero Here's why I was thinking ahead of the dividing by I was getting a little excited. I couldn't wait for this moment Minus five meters. That's that's the distance it traveled actually We need a better word in here We need Displacement yeah, that's better because distance What's the distance to New York City 150 miles? What's the distance of Montreal also 150 miles? There's no plus or minus on that there We needed the minus sign here. So displacement makes a better Better it gives us a more complete idea. And so what is that? That's minus 2.5 Did I do that math right check me with your calculator? That's Simply the average velocity between here and here. I don't care what else happened in between Well, I might care But it's not what we're concerned with it's not what I asked for I'd see let's see we got to do something more with this. That's just too dang simple What the heck do we need calculus for for that kind of stuff? That's just too darn simple Let's leave that out here. So we've got Let's make a little story out of this thing here Here's time Here's a position we can we can draw this out a little bit at Zero seconds. He was at three meters One second later. He was up at five meters So we'll call this one second that two seconds and that's all we did So it was up here at five meters that I Got numbers I better get units We didn't have numbers we wouldn't need units and Then at two seconds it was down at minus two meters into the depths We don't know any more than that But you got to figure know if this is a real object and it's going from there to there to there It's not going to do it in a jerky fashion Like that it's going to kind of kind of swing between the positions You know as if this is a turnaround spot It's going to kind of try to ease into it turn around the knees out of it Maybe pick up a little that's how you do it But what did you run out in the hall do some 1d motion for me? You'd have to do it something like that so maybe Something like that makes a little more sense of what really happened for the whole time Maybe more stuff happened. We don't know we don't have that kind of detail, but we suspect something like this So let's let's go ahead and say that's what happened Maybe there was a lot more going on But we'll leave it as something simple like that for now Here's the conundrum and this is exactly the question Newton asked himself This is exactly the question he posted on Leibniz's Facebook page and asked him Back in 1680 or something This is exactly the question That came up to these two guys having to the two of them independently They said well, I understand That between there and there its average velocity Was what did we have it two meters per second? I Understand that the average velocity was minus seven meters per second. I Understand that it takes a certain amount of time to go a certain distance and from that we got velocity I understand that but what Newton Enlightenment said is at any moment, though It's moving as I walk across the room I'm moving at any moment, but at any moment I'm not covering any distance So how can I have any velocity? At any moment proposed this Zeno proposed this No, not Jay Zeno the night the late night TV host Zeno the Greek philosopher said If at any instant we are not covering any time in an incident They're not covering any distance in an instant in time. How can we ever have any velocity? How can we ever go anywhere? When we can't go anywhere in no time and they couldn't answer that question No one could answer that question Zeno proposed it. I don't know what 300 BC or something Finally though Newton and Galileo. We're able to say Here's what we need to do Here's what we need to look at We know that Average velocity Requires a certain amount of time to travel that certain distance Nobody disagreed with that Not Zeno and not his grandchildren Everybody understood that no big deal what they couldn't understand is how can we go anywhere in no amount of time? So that we have any motion at any instant because an instant doesn't last any time Definition of an instant is it's too quick So here's what Newton and Leibniz did they did it independently did it about the same time Here's what what they said they said Well, we need to understand that that we're talking about Delta T being so tiny So amazingly tiny that it's really just an instant in time Delta T if Delta T was so small it would be and it would be a moment So they said let's see. Let's let Delta T Go to zero Let's let Delta T get so vanishingly small. We are indeed talking about an incident in time So we can then indeed talk about Motion and at an instant in time itself notice that I dropped this down kind of low Because the way we write it now is That we want to take the limit as Delta T goes to zero and this is exactly the question that Newton and Leibniz were able to now answer Because they started to formulate the question in this way You've seen this too. This is The instantaneous velocity notice the average subscript is now gone Instantaneous does this look familiar to you people? It's darn well better. What was the very first question? I ever asked any of you in fact I asked it by email over Christmas. What's the very first question? I asked about any of you I said everybody email and I asked you a question about yourselves. What was it? Have you taken calculus one? This is why? because this is Calculus and this was the question Everybody was asking up until then how can there be motion in an instant in time when we can't move anywhere in no time Yet, we know we're moving Every motion every instant Exactly the question they asked We're too dang lazy to write all this out every time So we have an alternate notation Let's convince all that stuff and say ds dt the time rate of change of The position is the velocity the instantaneous velocity. That's why I needed to have calculus. There's the first piece I'm ready to change up there Just to show you how fantastic we're lazy. We really are as engineers I mean think about how lazy an engineer has got to be who who who designed who invented designed a weed whacker That's lazy That's really lazy Leaf blower that's even lazier the laziest thing in the whole world leaf blower How many you got Joe three or four? Yeah That's how lazy we are We'll invent leaf blowers. This is even too much to write sometimes. So we have an alternate alternate notation We're talking about the position changing with time. It's very commonly understood if We just say s dot that that means the time rate of change of that value s we're having so much fun What's all right? We'll stop here because everything from here on Develops very very quickly anyway Remember though what we mean by the delta notation What remember what we mean by the d the differential notation the dot notation All the same stuff No, no, I said there were four things we're concerned with in kinematics There's the third velocity. We have time position and velocity and the fourth will hit on Monday