hello my name is mr cosnow and this is the first video in a series on kinematics kinematics is the study of motion without regards to forces so kinematics is simply trying to describe the motion of an object without any concern for how it started moving how it stopped or any of the conditions to actually make the object move another big thing we'll be talking about throughout this is vector quantities the vector quantity is of a value that has magnitude and direction associated with it now direction can come out in terms of north south east and west so you could say 60 miles per hour north but often we'll be dealing with variables that have one dimension that is to say they only go along one line like a train on a track so we'll use pluses and minuses to indicate directions so much like a number line there'll be a positive region and a negative region one of the terms to learn for us here is distance and distance is the total measurement of the motion of the object units would be in meters an odometer on a car would be a good example of distance now another term that will come up that's similar to distance but really different and that is displacement now displacement is a measurement from your final or your current position back to the origin so that would show up mathematically as a delta situation delta d equaling x final minus x initial the measurement in this case the units for it would still be a length measurement so we would be using meters now visually here's a picture of points a and b and you could walk along that dotted line and if we measured the length of that line that would be the distance you want however the displacement is a straight line between the two points and that would be their actual change in your position or in this case the displacement between a and b one of the very first things we like to create when we're talking about kinematics is a position versus time graph and this is the first of three graphs we have to help describe our motion now position versus time graph gives a representation of position associated with time and the graph itself can have linear and curved line segments it's really important to understand that when we talk about any of these graphs that the y-axis will be in the title first and the x-axis variable will be the second variable listed so when we say position versus time we realize that position will be on the y-axis and time will be on the x let's look at a set of data here we have time and we have position so our time starts at 0 seconds and goes up by 1 all the way to five so zero one two three four and five meanwhile our position would be our position from the origin at each of those time units so our position is initially at three meters at time zero and then moves to four at a time of one second it's at five both at two and three seconds then back to three at four and down to one at five if we were to plot this data for a position versus time graph it would look like this which i suspect you would have expected for the graph and if we take this point here two comma five it matches up with the data that at time two we are at a position of five meters if we pick another arbitrary point 4 comma 3 you can see once again it matches up with the data that at time 4 seconds it has a position of 3 meters so as we talked about if we're talking about a position versus time graph the y-axis is positioned so that's the y variables and the x-axis would be time as the x variables now in the graph there are various line segments and each of these line segments are going to represent a type of motion so let's look at a series of line shapes the first step would be a horizontal line a horizontal line on a position time graph is indicating to us that our position no matter what the time that position will be the same so if that's true then we must be in a state stationary condition keep in mind any horizontal line on a any kinematic graph means a constant so in this case because it's position time graph we're talking about constant position or the object is stationary let's go to a constant slope here you can see in our position time graph we start at one meter and we move up all the way up to 6 meters over 5 seconds now if we look at that we are changing our position in a certain amount of time and this change would be this constant change in our motion would be a constant rate in that change so if we look at our change in time and our change in position those variables are staying constant that ratio is constant which is why we end up with a constant rate of motion we could also end up with a curved line a curved line is a little really interesting because now while our position is changing the rate at which we're changing isn't the same so now we have a varying rate of motion and if we look at again the change in time and change of positions we end up at different values for each of those so if we take a look at a graph here that has a random you know lines drawn on here we have that blue line which has a constant speed because it has a constant slope and then we have a curved line which indicates that we have a varying change so that would go experiencing acceleration and then our line with that as the plateau there's a segment in there where the object isn't moving at all so now let's do a little check for understanding we have six line segments shown here a through f and in each of these cases a through f i want you to think about whether the object is at rest if it's moving with a constant velocity or is it moving with a varying velocity so take a moment and look at the six line segments and make a decision of whether it's at rest moving with a constant velocity or a varying velocity all right then let's see what we've got so if we peel back section a we find that as a curved line so that would be a varying rate and that would show that the object is accelerating section b that's a constant slope if it's got a constant slope it's moving with a constant speed section c is also a constant slope but interesting enough the slope is steeper so it must be moving at a faster speed right d is a horizontal line and we talked about horizontal lines would indicate constants so constant position in this case would be a case where the object is stationary line segment e again is a constant slope but we realize that this slope is a negative slope so it would be a constant velocity but it's going to be in the negative direction a different direction much like we talked about earlier keep in mind that vector quantities have magnitude and direction so this negative value is indicating a different direction for us and then finally section f has a curved line so we'd have a varying rate so once again there would be acceleration involved i hope those cleared up some questions for you and you got some good answers this completes segment one of the videos thank you hello i'm mr cousino and this is the second video on kinematics in the previous video we looked at various definitions for terms that are associated with kinematics and also looked at a position time graph and the various line characteristics on that graph now talking about lines and the characteristics one of the most important things we will do when handling and working with kinematic graphs is solving for slope now slope is what you would expect it to be what you learned in math class that slope is rise over one so delta y over delta x the slope at a position time graph provides us some very important information and what we want to take a moment right now is really look at what does the slope on a pt graph give us so let's say we have this position versus time graph here it happens to have a curved line and we're arbitrarily going to pick point b and solve for the slope of that line because at that point it's not a linear line we can't pick points on the actual line that we're looking at we need to draw in a tangent line and have that tangent line touch our line at only one point that now gives us a new line to work with but a line that actually has a constant slope and is linear so to solve for the slope of this blue line the tangent line we're going to need to pick two points on the line so i've picked these two points right here one just before p and one just afterwards in truth those two points could be anywhere on the line on the tangent line because that whole line has a constant slope throughout now to solve for slope we're going to have to look at our rise over run so we'll measure the actual change in the vertical direction that delta y we'll get a number for that we'll then go in and we'll measure the change in x so we'll measure what is the run and now we have a delta y and a delta x we divide those and what we really have is a change in position over change in time and if we look at that name we quickly realize that's the definition of velocity velocity is the change in position in change in time now velocity has units of meters per second for us you could also have kilometers per hour miles per hour if you're in the english units but ultimately it's a length per unit time mathematically in a simple form it's delta d over delta t before we go any further let's make sure we remember the fact that speed and velocity two words that sometimes are used interchangeably are similar but they're not the same speed does not include direction but velocity does simply put velocity is a vector quantity it has magnitude and direction speed has only the magnitude so on the highway when you read the speed limit it is at let's say 65 miles per hour that sign is actually quite true it tells you what the speed you can go 65 miles per hour it's not a velocity limit because it's not actually telling you a direction that you have to go it just tells you how fast you can be going now one of the key terms that's going to come up in our work with kinematics graphs is this idea about instantaneous so right now we're talking about velocity so here we have instantaneous velocity instantaneous velocity is the velocity of the object at a specific moment in time in order to solve for the instantaneous velocity you have to actually solve for the slope at that point so you need a tangent line to solve it the speedometer in your car is the instantaneous velocity it tells you you're actually the instant speed but will associate the direction based on which way you're going but it'll give you the instantaneous value the speed the magnitude at that moment in time mathematically it shows up as v instantaneous equaling dx over dt this is the beginning of calculus force this is looking at the derivative so that d is a mathematical representation of talking about looking at a infinitesimally small amount of time that's what those little those are those d's are indicating now there's also average velocity now average as you would expect is the mean value velocity of the object over a period of time this time though we need to solve for the slope that connects the two points that we're looking at and mathematically that shows up as a delta delta d over delta t that delta says that we could be looking at a very large unit of time if we look at a position time graph and look at how we could solve for the average velocity from point a to point b we would connect point a and point b with a line and solve the slope of that line between those two points and if you look at the line segment the blue line as it goes from a to b just after point a the slope of that line is a negative and then it goes down to basically a zero and then it goes up with a positive slope and increasing to a very large very steep slope all of those numbers averaged together would give us the slope of the line that connects points a and b and mathematically again that shows up at v f equaling delta d over delta t this completes the second video on kinematics thank you hello i'm mr casino this is the third video on kinematics in the previous two videos we defined various terms associated with kinematics we looked at a position time graph and we also discussed the importance of slope when working with a position time graph let's move on to the second graph in the family of kinematics graphs and that is velocity versus time now for velocity versus time it's really just a visual representation of velocity associated with time and the graph like a position time graph could have linear curve line segments but what is unique is the data points used to construct a velocity time graph are the instantaneous velocity values from a position time graph so you need to go through and solve all those instantaneous velocities match them up with the given time and you end up with your x and y values to make a velocity time graph so let's say we have this velocity versus time graph again it's a plot of a series of time values matched up with the instantaneous velocity at that given time so if we arbitrarily pick this point right here at time of 8 seconds we see that the object has a velocity of 30 meters per second now that point is telling us that at time 8 seconds if we went back to the position time graph a tangent line at the 8 second mark would have a slope of 30 meters per second like position time graphs velocity time graphs can have various line shapes there can be horizontal lines there can be constant slopes both positive and negative there could be curved lines in this sample velocity versus time graph we don't happen to have any curved lines but we do have various constant slopes and even a horizontal line in the beginning from 0 to 2 seconds it has a constant positive slope so the velocity starts at 0 and increases at a uniform rate up to 2 seconds it then continues to increase its velocity but now the rate of increase is greater than that in the first two seconds and it's greater now as we get through the move through the next two seconds up to four seconds from four to five seconds the velocity remains the same before from five down to eight seconds it goes through a negative slope so it actually slows down to zero but then increases again in a negative value up to negative three meters per second at eight seconds and then finally from eight seconds and beyond it remains at a value of minus three meters per second a couple interesting things to note that horizontal line between four and five seconds does not indicate the object is at rest but rather it's moving with a constant velocity the same would be true from eight to ten seconds in that line segment it's moving at a constant velocity of minus three meters per second for an object to be at rest on a velocity time graph the line needs to be at the zero mark at no point does it actually stay at zero but it does cross zero twice in the very beginning at time zero it's at zero meters per second which is to say it started from rest and also was at rest for an instant at seven seconds now solving for slope on a velocity time graph again rise over run same thing delta y delta x is also going to give us some interesting information about the graph if we think about the definition again now we're looking at rise over run this would be actually its change in velocity and change in time that is acceleration keep in mind that acceleration is a rate of change of velocity therefore any acceleration is a change in velocity so you could be increasing your velocity or you could be decreasing your velocity the word decelerate is often used as such for an object that is slowing down in this class we won't use the word decelerate not that it's wrong but acceleration already covers it so i want you to be comfortable with the idea that acceleration isn't just speeding up it is also slowing down like velocity we could also have instantaneous acceleration to solve for instantaneous acceleration we go through the same procedure this time we'll solve the slope of a tangent line on the vt graph and again it's a derivative where it's dv dt and we're looking at infinitesimal change in time to get the actual acceleration at that instant we also have average acceleration this would be the mean acceleration over that period of time and again we're going to connect two points on the graph and solve the slope that connects those two points and mathematically a average acceleration average would be delta v over delta t the acceleration versus time graph is the third and final graph in the family like the others it's a graphical representation with acceleration associated with time the graph can have linear curve segments and now all the values for acceleration are the instantaneous values taken from the velocity time graph so you need all those small tangent line solutions at each point so if we look at an acceleration versus time graph here this one happens to have a constant slope the object has a acceleration of one meter per second squared at time zero and increases up to six meters per second squared at 5 seconds if we pick this point 3 4 what we are saying is at time of 3 seconds it has an acceleration of 4 meters per second squared if we went back to the velocity time graph at time of 3 seconds the slope of the line the tangent line at that point would be 4. so those all match up and work backwards in the same way that completes our video series on kinematics i hope those were helpful and we'll see you in class thank you