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graphing lecture

Added Sep 08, 2020 •

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start off today by watching a review video we want to get into graphic and how graphing applies to physics we're getting into it today we're going to get into on computers tomorrow analyzing some ocean one stop or not and then Monday we're going to be breaking out the tracks in the carts in the motion detectors and you're going to be doing a lab regarding graphs of a moving car and identifying what a car's doing days on the grass a little review is a teacher for Bozeman Montana I sent you a video he does a great job of putting himself in the corner and showing you the truck they're made by students in my high school science class when I tried it play there data in a graph Elementary School from middle school to high school another color if you don't spend very much time on Superdry to know how to do it put this video together to show you the importance of grass the different types of grass the first molar started with the term guard Community Church Angel Ramirez Central leaders graph plot basically ways that you can take data and display visual well let me give you an example this right here is Charles David Keeling spent years and years in the Hawaii collecting data the levels of carbon dioxide in the atmosphere show you love someone when we get there numbers but if I were to show you all the data to mr. q and collected we would find Healing Kirk and this is one of the most famous grass in all of science is basically showing increasing levels what side is the annual cycling of carbon dioxide this is very important cuz it's tied to global warming and so when we can see the data we can make sense of it. There are five major types of grass that I can talk about in this video they are limescale the one start with a little pretty quick and see what you know right now so you can write and what about the farmer went to the bar graph and histogram and hopefully in points you than the pilot did you do did you get all those right hopefully the ones that are confusing I understand a line graph is going to be. Connected with a line even though we have a best fit line here that scatter plot is is not going to connect about the dogs and she'll core did you get screwed up on the bar graph how do we tell the difference between a bar graph and histogram and bar graph for going to have space between different columns in a histogram are going to watch and so important the elephant if you're going to collect that and then you're going to have to choose what grass you're going to use another word for the data always comes first then you got to figure out what grass you're going to use and full of talk about different first one is going to be a blind rapper going to use the line graph and we're looking at change over time until this one we're looking at us trade in goods and services and so you can see that the dates are going to be a long meeting in the morning Zion's maybe we're collecting data on an individual worm and how much oxygen it requires overtime for consumed overtime in the line graph but they were looking at a scatter plot we're going to use that correlating to number set for two sets of data so the correlation of variables inside the scatterplot right here they're looking at the eruption of Old Faithful along a Direction Take and then to the time between science classroom forever very one variable independent variable and the dependent variable in a scatter plot NBA draft choices when you're doing that make sure they can put the independent variable on the x-axis so let's get this plant right here I'm doing an experiment where I buried him Rose over open the I'm burying the independent variable X the amount of fertilizer and then we put plant growth on the why we look at a correlation to community credibly important Barbara music comparing two groups together or more than two groups in southern this bar graph for looking at worldwide incarceration rates and we're comparing different country and have different colors of light affect the rate of photosynthesis looking for the rate of photosynthesis on the y-axis and then we represent each of those different colors of light using the different fall off of bar graph that far is going to represent average Instagram we're looking at the distribution of death look at Instagram here we're looking at a height of black cherry trees we have different heights along the bottom and so for example how many of these cherry trees are going to be between the height of 7275 while we look here and then we find them unless they were graphing human title on the bottom Instagram you that forever looking at parts of a whole these are all the different families of wrote and then we can see what percentage of those are the different no mirror it is going to be most popular those are going to be okay once we got that then we can actually get to the graph to let's play with that person but then I've got data from a pretend ice cream store that I have here in Bozeman and on this data right here I've got the average high temperature in Bozeman and then I've got the number of the look I wanted to display for example all the different month and then the percentage of the whole of which I told ice cream I've been looking at a pie chart of all the different ma as a different section of the whole pie over time look at the average temperatures the average high temperatures in Bozeman what would I use of the airline will they want to look at the free specific month Karen ice cream sales in all months that start with the letter j left Barbara what you doing call the elements of a graph correlation of ice cream sales how would you describe the important parts of scatter plot in you want to do if you want to figure out where your actions are going to but I got to put along the x-axis in the foot temperature to put my ice cream sales on the wall by measuring it in ice cream sales Union Bank what's the next on a graph the next is going to be the title the title should tell you everything contain with them what was I going to look the correlation of ice cream sales and average high temperature it's like weird is the movie the date for that what time is The Peddler to simplistic you'll have a title this beautiful lady ice cream I should be able to look at the title what's the high score on a scatter plot we're going to have the data and then finally we should have a best fit line best fit lines going to be like an average of the Death Cure putting it in freehand basically time for the the dots on your Scatter Plots to be best it might never extend past your dad I can put like an arrow on the end of it because really I can only put a best fit line within my dad I can only interpolate with you believer elements of a good title label the axes make sure you have linear number so you just going to be here that is 15-15-15 with teeth between major gridlines and we're going to the same thing here in Hawaii but all those are all the graph another student to do if they want to include the number zero. collecting data that affects plant growth are number one must start with the type of descriptive the title should show me what's going to be on my ex and what's going to be on my y-axis select a relationship or the relation of fertilized I'm next Plant I hear but since I'm burying the amount of fertilizer like independent variable to be down here so we would want fertilizer to be down here and then we want plan type 2B on the side so we would have planted over here than fertilizer down here is in the scatterplot that you should never connect other things we have non linear scaling so that he has 5 7 11 15 17 19 the distance between each of these to be equal you can also see that the best fit line is extending past the data so this is a bad stand for we're having to try to remedy that when you're making it's electric okay it's all that video hopefully that's just gave you a little refresher of a grappling is important than a little you turn on your life but actually you're going to get you a new mathematics called calculus calculus is based on the method of graphing to find a slope area under a curve now on a graph that's pretty easy you know you draw a line and find trying to find the slope of that by doing rise over run that'll be doing today but how do you do it if you don't have a graph if you just have like a expression for a line like y equals MX plus b how do you find slope in a formula West slope in life with a knife changing all the time well what you do would you pick one point on the curve and you draw a line called a tangent never heard of his hands and yet Madeline is such a sucker for a circle only one point you know if you have it you will eventually you can find the slope of a tangent of a curve using a method called a derivative in calculus it's how you manipulate a mathematical expression did the same thing you do on a graph if I hit a curb and I how to find slope tangent and find the slope of that line there's a way to do it with mathematics to we're not going to do with the mathematics way in here the calculus play I'm going to show you how to do it yourself grass but remember when you take calculus and you talk about derivative I think that between slopes in this class so now you're going to look at some of this song we always start with the basic I want to see open to everybody know and then we build up from there so let's start this out are graphing know by the way let me show you what these nodes are intended to be like so your nose are couple of pages here a front and back of a single page but it's meant to be on the website astronaut because that one that was up there wasn't complete but I need to give you another page if you did okay or two pages on one sheet and faces on back of the heel Sofrito probably like this out of your printer now these are designed these are what style of Hill City Cornell so you're familiar with this the way I do this to it and then side over here which is to your left do you use those as quizzing yourself before the test try to answer those questions hey if you can't answer it hears the answer right there all you do is open it up and go oh yeah so that turns regular nose into a and I'll tell you the hardest thing in here and how do I get there to test if there's one tool for you so and you'll see how easy it goes today with the villains you have so let's start from some place at common ground for all of us I think that if you're in this class Advanced physics you should already know that we call the lines on a graph x-axis and y-axis you probably know well beyond this that this isn't the only place that you can put information there's also a quadrant over here down here and over here on a regular X Y on it what number to three and four quadrants is that only use quadrant one in this but we're both of our things are positive so vertical horizontal these are terms that you should be familiar with X and Y axis that should be something we're familiar with so let's build off of it and see where we can go now you mentioned about the pendant in Hindi find a variable truthfully that's not always important what's important is creating graphs that are meaningful so regardless of time being the dependent or independent if is the independent it goes Mac. anyways but it is the independent talking about school so these notes have areas for you to fill in you need to be filling in these blanks so you're going to have no set up like them so you're looking for most of the time up here you'll see if they uphold face underlined word that would be blank on your sheets oh you can talk to it monitor so you still in the worst time their time is on the x-axis have you ever heard of this smoke rise / rise over run Daddy's rise / run okay so what's the rise done this graph can you tell me what it is or is it like so we know if we're going to do is slow which is Rise / run if it rise / run that means that we arrive / time something divided by time so this bloke is something divided by time we have a special name for things of year that are divided by time first test question real numbers cast a race and his class is something divided by time we might want to put when I say that you should be putting a star next to that thing that I and put the word cat so you know before the death you got to go and refresh with that more before Christmas when I say testing testing for quizzes anything divided by time ring I'm going to battle a little bit when they a teacher that taught you something they're trying to keep something right by plant when I'm wrong they probably talked to this rate is distance divided by time anybody heard that one before okay I'm glad some people are going to go because you don't have to battle against learning that a little wrong distance / time is something being divided by time distance divided by time are we dividing something by time tokenpay it's a rate are there any things I can / time / speed by time does he has to be changing over time is that the same rate in distance divided by what is called speed just called acceleration they are not the same race we cannot just use the brand firm rate equals distance divided by time that's all money is a nickel are there more types of money out there that nickel there's more types of REITs out there than just distance divided by time there's speed divided by time there's some money in my bank account / time there's the heart rate in your body now the rate of the pounding of your heart / time that's another rate all of these multiple have specific names like heart rate distance divided by time we don't just say rate we say what rate is the watch that the word rate is very general when you talk about one specific rate like distance divided by time we got it now getting specific that's not just any old rip it's already called okay so little bit of vocabulary there is coming after you is easy one thing that he mention is at the scale has to be linear when he was telling you about problem on a graph I don't use that I don't say it's supposed to be linear they say it's supposed to be consistent I think it's distance is also one of those commonly misspelled words that people put in a instead of an e at the end app for Content a lot that one so what does the word consistent mean to you repetitive repetitive just like you're being so it's repetitive and it's the same rack tell me what's not consistent with those numbers on the bottom who can identify was not consistent with that shop Miss a Thing John just tried a little bit more put together and I couldn't wait to hear one unit is one box then all suddenly here in from 1 to 2 is still one unit but now it's two boxes as an inconsistent scale for some reason I see this a lot with student that they started 0 in the corner and then they always March 1st and then we'll go like for over in March 4 / an R34 over and Mark 4 bull that first part is should have been for over till your mark one. One box so I don't know why this happened it's a great mystery to me but I seen a repeated by students year after year at how to make a pillow for some reason that zero to one my. Always being One mods if you don't have a receipt to scale your graph is worthless about slope formula have you seen slope formula like this before what is the math formula to find slope of a line using X1 y1 and X2 Y2 what do you think the one in the 2 stand for in here first point and second point now what do we call it when we write a number or letter below are normal numbers and letters Our Lady of Lourdes English like if we were going to put it in Microsoft Word number to get her something some kind of superscript that's what does sub mean above above your right so here you see subscripts when we do pop when we do powers of 10 will be using superscripts like 10 to the 3rd power 10 to the 4th power show me the subscripts and superscripts in here this happened she would lie to those are the coordinates of our second point I want those according to Harper's Point I'm pretty confident that if you hadn't seen this stuff before this exact way that you seen the way and that this is understandable with you if it's not I might have some problems I assume you have some background knowledge that stuff on that first page you should have seen now that doesn't mean you're not going to be successful versus time his always lie versus at that means the first thing goes on the y-axis the second thing goes on the end if I tell you to grab distance versus time what goes on the y-axis distance hey can you give me the slope intercept formula of a line in math class what's the slope intercept form of a line in a math class play wait say it again would you start with why right when we say slope intercept you start with y equals when you do a title for a graph y as a function of that's what your people sign in the needs of the function on the other side you do something to ask you X and then you add people so it's y as a function of x Y as a function of X Y is other on the y-axis are you home he tells you what goes where you don't need to ask me if I give you a call a lab on Monday and I say you have to create a distance versus time graph to the cart you know those on the y-axis in Excel alright so some basics and now we're getting into the Pacific slope of a distance versus time graph this is what today is all about how do we look at a distance time graph look at the line and figure out what the object doing so remember some of those words there are to be filled in on new sheet so what does the slope of a distance versus time graph it represents the average speed of an object speed so slow cook a distance time graph tells us how fast what's the formula for slope what over what rise over run what's on the rise on a distance-time graph distance what's on the Run / time is it a rate does it feel hot but can we just call it right now we got to specify what rate it is its distance divided by time we call that rate speak so let's start a dialogue Raptor comes to visit I actually be too difficult for you. Doesn't mean it's not Advanced physics but don't think that the stuff in here that you get Ghost this is easy so what does a straight line mean on a v vs T graph time if that would be girth and I jumped on the flying with a skateboard how would I move but I move on my own any Direction no because there's no what there's no no speed so if you see a line with no smoke I need this object to stay in the same place the whole time like if this is 10 is 10 meters away send me away away away it's just not the same so are these straight lines on the one on the right they are straight is the slope constant or changing this is where you have some some people have problems they'll see it going up and no say is changing but I'm not asking you is the distance G I'm asking you is the low changing that means life is Upperline to slope in the beginning is like this the smoke at the end is like that did it change no that's called what kind of slope if it's not changing Mountain slope. Sloped on this wrapped up in just being slow but being so constant slope means what kind of speed and speed these things are moving can you tell me which one might be moving faster how to get on a skateboard on each one of those Plumbing more slope sombor slope mean more speed you're starting to analyze these wraps now these are very basic straight line so let's spoil this down to this on a distance versus time graph if the slope is constant speed is constant I think that's going to fill out the front page of the note we're going to put the key back how is it going with these notes so far you've been able to pay attention to me is there been a lot to fill it up there a lot of things so this is how it goes when you have Dylan note imagine trying to do all this stuff do I talk that do I move fast through the notes and stuff yeah I do and I know that it's part of this course having these notes will help you to deal with with mister Ben's is inability to slow down Okemos today so we did straight line distance versus time graph a curved line will be so what does the curved line on a d vs T graph mean Annie's real accelerate non constant speed last time we had a straight line constant speed constant so this is a non-conference and constant what's take a look at these two graphs let me get something I can maybe make us a line that you can see with trying it on there I'll just do it with me. so here we have a a grab is this line of constant lower changing slope changing at the beginning it's like this at the end just like this what happens to the slope is it is it getting is it in is it increasing or decreasing increasing or decreasing sorry creepy 360 what we call that acceleration really really slow and at the end it's like this what's happening to the slope in degrees decreasing so if we have decreasing slope we have decreasing speed we have acceleration it's going it's not going up it's going so instead of using positive we use negative we have acceleration but it's not called positive acceleration and physically really don't use the term what's another word for this a normal people use when you're slowing down acceleration in physics we say negative acceleration acceleration means the speed is changing negative means it's going down so there's two types of acceleration positive and negative positive is feeding call we can use the term deceleration in here to I tend to not use it tomorrow so realize when I take negative acceleration and your brain that she connected deceleration all right got some skills. Now let's make sure this is pumped up a little bit if the slope is changing we noticed he's changing well there's two ways for the slopes change to get an increase as in this one or it can decrease as in that one so what is this one mean when it's increasing and we have an increasing slow because slope is speed how to say increasing acceleration or more specifically positive and conversely what does it hit the curb is getting less now there would be a decrease in slow decreasing slope that's pretty much the meat of the disc versus time graph analyzing is something to staying still moving at a constant speed for speeding up and slowing down take a look at a graph little may be hard to see from the back of the room can you see up an upper left hand corner there's some writing on the strip small letters with the first three letters what do you think yeah everything up here you might not be able to see it because DVT that's another way to say a distance versus time graph DVT what does it say after that what the Ferrari what's a Civic my car is so hot so we got to that have a distance versus time graph what their distance units yard not labeled we might assume that they're either seconds or maybe tenth of a second or something I don't think I'm going to be 10 hours are in 1 minutes with a moving car so we don't know if we can't really do any analytical analysis of this week and take numbers and find a slope we don't have coordinates to the bottom we don't have any given measurement tell me what's going on is this a con can you float between these two dots and look pretty pretty say something and then we see that the slope close to my house what's probably Happening Here decelerating or negative acceleration is slowing down a little bit maybe they're shifting gears sometimes in the car when you shift gears you don't have the gas on you slow down a little bit and then you get into gear and you pick it back up to higher speed yeah they're starting behind the starting line so that the Ferrari does up here at the starting line the Civic back here the Civic starts going what happens when the Civic get to the starting line what happened to the Ferrari so they're trying to get the Civic Head Start it looks like you get back there you can go in as soon as you pass the starting line for our he's going to start going let's see how long you can keep in front of the Ferrari so you just hit on what's probably going on here we can also look at that and Analyze That Straight Talk tell me about this constant slope compared to this one which one is greater a or b b is Raiders coldest it's going greater speed and then it slows down again because from this to this so I don't know what happened here but it's going slower at that point tell me about the Ferrari from this point to this one where you going to snow ski but if it stays constant 0 it's no slope no seed that is constant but it is also you should identify the snowspeeder right here to write what year did the Griselda look at this line from here to here does it go straight to you and can you tell me about the speed of the Ferrari over that portion yeah finally the Ferrari is it a point where is it the same distance away from the starting line at Pacific and then after that but Ferrari is further away from the starting line when the Civic at the same time so that he's out front so that at that point the Ferrari has caught up to the deck now Staffing it and it looks like the Ferrari is able to do a much bigger acceleration and we see the Pacific too but we don't see the beginning of this sitting here celebrating up to speed so we can easily tell something about this crap either account now last thing I want to add to these notes today before I show you how to do your homework is this Malaysian and extrapolation circulation and extrapolation more extra pollution and interpolation any idea with the prefix extra might be more Beyond above right can side with in I think yes it was full Asian is kind of a 34 yeah on a trip on a good kind of like that so these are kind of your data that would be on a grid that we Mark the. This is beyond our. what is this Hidden Side of our. But regardless of which one it is it's an educated guess they're both doing the same thing they're just identified a little differently because one's going beyond your data and sometimes but we do it quite often so Revere star in a cage welding a five pointed star indicate if I was to graph a function that the black dots that are on there and I say hey look like a straight line I'm going to connect them in a straight line I might say what are the coordinates of this point for this point so if it's legit this time maybe I can see how far the car goes in a certain time I can find the distance it would go beyond what I measured or within what I measured maybe I can go up and over in determining distance something's going to tell me to do in my lap but I could have done you something you'd put in your  if you were able to do data off your name down here you're probably able to do about the test of the middle the extrapolation off and on your system will not let you test that that's why I didn't powerful tool we can go beyond laboratory and expanded function of a drive to something that we couldn't do in your we could measure how how far apart would go in like maybe two or three seconds but if you think you can follow a car for an hour then now you can run into walls you're going to run into all kinds of things around the campus can be outside this room but we had a graph weeks to extend the graph all the way out time to an hour and they can ask him if things were in the way how far we go. okay so next let's go through what your homework is tonight the last page here are you going to actually determine a slope I'm going to go through it a lot more indefinite expect you to do when you show it to me I'll tell you what I expected first of all finding the slope of a line pick two points on a line now those two points should not be near each other they should be pretty much as far away from each other as you can when I want a new line one of the other that reduces your hair so I got 2.1 any chat now what I want to do is try to get the X and the Y coordinates for each point there should be something you've done ended in math Bridgeport police officer doing this for a while so you better have the units these are measurements of time and distance not just number so I have to make it a point to be 2.4 seconds 2.6 meters you might have made a difference. Okay and 7.6 labeled on here sheets you should label them Soldier 24 seconds 2.16.18 22 seconds 7.62 4.2 okay the next thing that we would do is not this this is not something you would do if you would do this on the graph identify the points but I want to clearly identify the point through this first time X1 y1 is that 24 seconds 26 years and asked you why he was at 8.2 seconds to 7.6 the next thing you would do to determine a slope is to write the slope formula in here y'all have to start with the formulas don't put numbers in until after you've identified the formula I put Adam what does m stand for in a math class 4 equals MX plus b so here I use them for sloped what if I use them for here meter same as me and different things call me Millie as a prefix and it gives me mask as a as a variable Soul or do you want talking about so you start out writing is Y2 - y1 / X-2 - X1 and then you would plug in your information straight from your points up on your draft and now I wouldn't do this next part down below I would do it right after this part that we just did so I would not write any of this I would actually put an equal sign next to this and put equals 0.86% I'm just showing you that this is what you get when you subtract and then if you divide those that answer you don't need to show those intermediate calculations in here you need to set it up set it up plug in your measurements and then generate an answer with unit the one thing you might notice here is that the slope in this class has meaning it has units rocking office do I identify what information with social telling us what it is on this book Kneaders how would you say meters per second is that sound like miles per hour what mile per hour unit of speed is the distance divided by time you guys didn't try by time you got to be

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