all right this video is about how to analyze position versus time graphs so let's imagine that you have a car or that you're watching a car kind of driving down the street okay just outside your house or something and you take uh say you have like a measuring the device um and a stopwatch and what you're going to do is you're going to see how far does a car travel for each second of time and depending on if it's going forward if it's going backwards whatever you just want to take some data and figure out okay what position or what distance is the car traveling over any G given period of time so for example let's say you do this you set up a little data table time time versus distance in meters okay and let's say you go okay 0 after 0 seconds the car is travel let's say it's our starting point 0 m after 1 second let's say it's traveled 15 M after 2 seconds let's say it's traveled 30 3 seconds 30 4 seconds 20 and 5 Seconds zero so here's your data that you've collected and what we're going to do now is we're going to go ahead and construct a graph of Time Versus distance uh and often times we'll refer to this as a position we should do that but you could use distance as well and yeah so we're going to go ahead and set up this graph so why don't you push pause and graph this yourself and then when you're ready come back to the video all right so here's our position versus time graph um shape like this and so one of the things I'm going to ask you to do anytime you have a graph with lines on it actually what do you think I'm going to ask you to do find the slope so anytime there's going to be lines on a graph I am going to ask you to find the slope and we'll use that to help us analyze that so let's go ahead and do that let's find the slope it's too big isn't it let's find the slope for each segment so we're going to go ahead and find the slope for each segment and by segment I mean each kind of time segment here so for example you could do it every second like 0 to 1 1: two and so forth but um you don't have to do that you can just do when the slope is constant so we could go from 0 to 2 2 to 3 3 3 to 4 and 4 to 5 so we really if you look at our picture we have four different slopes here all right and how do we find a slope rise over run okay so the generic thing we say rise over run right right or Delta y over Delta X that's our slope so let's go ahead and do it for this one so we have Delta y over Delta X so our Delta y here is 30 so we're going to go ahead and go 30 m minus oops 30 m - 0 / 2 - 0 seconds seconds and we get 15 right and what are the units here m/ second so what can we learn about a veloc uh position versus time graph the slope tells us what the velocity yeah so our slope here is going to be equal to our velocity all right so 15 m/s and really you can see that from the graph every second we're speeding up by 15 or not speeding up every second we're traveling 15 M so 1 second worth 15 m 2 seconds worth 30 m all right um okay what about 2 to 3 so notice at two we're at 30 and at three we're at 30 right so when we do our slope what do we get zero 30 - 30 3 - 2 gives us zero right 0 m/s so what's happening there there's no movement at all right what have we done stopped okay so at that point in time we have stopped right so we're at 0 m/s here by the way it's a good idea to take a look at your graph and you know we generically say slope is Delta y y Delta X but in this case we have meaning of Delta Y what is our y AIS position or distance right so I could write that instead of Delta y generic we'll write it as Delta D and what is our xaxis time so instead of writing Delta x what could I write time or delta T and what is Delta D over T velocity yeah so Delta D over T is velocity so we can use that to help guide us when we're looking for meaning of slopes all right let's keep going actually why don't you keep going you guys should be able to do the rest on your own go ahead and write those out calculate those slopes remember you always do final minus initial when you do your subtracting when you do your deltas okay and if you could can you write the physical meaning of these so for example zero we said the physical meaning was we were stopped what's the physical meaning of 15 -10 and -2 go Ahad and just write it on your paper and then we'll discuss so what's the physical meaning of the 15 we're moving forward then we stop then what do we do now we're going backward good so in this case we're going backward forward here we're now moving backward what about - 20 we're also backward now what's the difference between the 20 and the 10 and the 20 faster right so we're both going backward and both but this one is faster all right so the last thing I did want to uh discuss on this is what is the meaning of the steepness of the slope okay yeah how fast it is so in other words a steep slope means what steep slope means well fast okay or faster the steeper the slope is the faster is in fact if you have a slope that's horizontal how fast are you going you're not going right you're stopped so you can see here we're at 30 m and here we're also 30 m okay all right so here's my lowbudget video for this problem um I found this old car for my son's toy box so um anyways let's just look at what's happening we have our car right it's at 0o MERS and in fact the car is looks like it's already moving at 15 m/ second and it's going to do that for 2 seconds so we have our car traveling here 15 m/ second this would be 1 second this would be 2 seconds and at 2 2 seconds the car actually stops for a second right and then at 3 seconds he's going to go in reverse now he's going to move slightly slower 10 m/s in Reverse this time and then at 20 M he's going to speed up to -20 m/ second and in fact at 5 seconds he would be back where he started at the 0 point um and then we don't know what happens at five he didn't necessarily stop there he could have just kept moving and according to the problem you would probably just assume that okay