this video I'm going to give you an integral to linearization or curve straining we linearize data so we can easily fit a line to the data and use that equation to make predictions a linear set of data is easier to work with any curve set of data first we're going to practice writing physics equations from some data that is already linearized so what do we need to do to linearize and graph that is curved this first one is an inverse relationship so we are going to graph the Y so the same data that we have on the y axis and then the X data so all the data points down here we're instead gonna graph 1 over X so we're gonna do 1 divided by every single X so we're gonna take the inverse of every data point on the x-axis and then we're going to regrow fit with the Y data on the y axis same as before and 1 over X data on the horizontal axis the next one's a quadratic we're gonna do something somewhat similar but we're gonna do Y verse x squared so we're gonna square all the X data and the last one we're gonna square all the Y data and then we're gonna leave the X as it was another option for this last one is to leave the Y as it was and we could take the square root of all the X data that would also work for this square root graph once we linearize a graph it's not still y equals MX plus B no you can't use your original Y physics variable and your original X physics variable so this first one if we graphed Y and X which is normal we get y equals MX plus B and remember Y stands for some physics variable that's gonna be on your vertical axis and X stands for some physics variable that's gonna be on your horizontal axis but now if we change that we're graphing y versus 1 over X we can use Y equals M times 1 over X because this is the variable on our horizontal axis so whatever's on a horizontal axis needs to go in the x position in y equals MX plus B and you'll see a pattern here where we're replacing whatever we changed with the new variable so we're gonna put the new physics variable just with its squared or square root or whatever it is in the spa in the equation if we graph something Y squared versus X and then we just write y equals MX plus B that is not the right equation that matches the graph because the graph has a y square not students mess this up way too much so you've got to be careful about that all right so this page should be somewhere in your packet and maybe in a reference packet or maybe in your main pack up you should find that before continuing the idea here is we aren't gonna do the steps in linearization the actual square in a square rooting or inversing but we want to show you the ideas what you would do and then how you would write the physics equation so the initial relationship is quadratic so what needs to be done to linearize a quadratic curve you're gonna square the horizontal variable in this case it's time so we're gonna go over here and this it's gonna turn out to be a straight line we still velocity on our y-axis and on the x-axis we no longer have time we have x squared you have to write x squared you have to have the unit squared as well that's super important by the way these relationships are just made up so there's we're not getting into any physics behind this the units of our y-intercept are the same as before meters per second and the units of our slope are the units of the Y meters per second divided by the units on the x-axis seconds squared so if you look do your fraction algebra that's meters per second cubed so our physics equation is going to be the Y variable is equal to the slope times the X variable plus the y-intercept it's a Y variable velocity is equal to the slope including units times the X variable which is x squared plus the y-intercept which is negative 3 meters per second so there's the first example next example this is a square root relationship so we need to square the velocity you will need to know what to do with that so there's three different options and you need to know those you won't be given the reference packet for quizzes and tests when we square the velocity which is on the y-axis we now have velocity squared and those units are squared as well so V squared and it's meters squared over seconds squared the x axis does not change time in seconds the slope is meters squared over seconds squared over seconds and so there's the units for the y-intercept and if you do our fraction alledge where you get this so the linearized physics equation pause the video write your linearized physics physics equation and then come back and check your work y-variable slope with units x variable y intercept with units we'll do one more I might pause the video do all of this and then come back and check your work it's an inverse relationship we need to graph one over the variable on the x-axis which is time we're gonna have velocity still in the y axis because we don't change that the x axis is now 1 over time now double check make sure you actually did that 1 over time and 1 over seconds if it's not both 1 over time and one over seconds it's not correct the y-intercept units meters per second now the slope is meters per second over 1 over seconds you do your fraction algebra comes out to meters and the linearized physics equation y axis variable slope with units x axis variable 1 over time plus 2 meters per second the y intercept this physics equation now works just like any other you put in the time gives you the velocity at that time you put in the velocity gives you the time at that velocity this is all just made up numbers and data so this doesn't actually help us predict anything but that's the idea behind all right that's how you linearize data