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in this video I want to talk a little bit about acceleration acceleration and this is probably an idea that you're somewhat familiar with or at least you've heard the term used here or there acceleration is just the change in velocity over time change in velocity velocity over time probably one of the most typical examples of acceleration if you're at all interested in cars is that many times they will give you acceleration numbers especially for sports cars actually all cars if you look up if you look up in Consumer Reports or wherever they give the stats on different cars they'll tell you something like I don't know like a a Porsche and I'm going to make up I'm going to make up these numbers right over here so let's say that we have a Porsche 911 Porsche 911 they'll say that a Porsche 911 they literally measure it with a stopwatch can go 0 to 60 miles per hour and these aren't the exact numbers although I think it's probably pretty close 0 to 60 miles per hour and let's say 3 seconds in 3 seconds so although officially what they're giving you right here are speeds because they're only giving you magnitude in no direction you can assume that it's in the same direction I mean we could say 0 0 miles per hour to the east 260 miles per hour to the east in 3 seconds so what was the acceleration here so I just told you the definition of acceleration it's a change in velocity over time so the acceleration and once again acceleration is a vector quantity you want you want to know not only how much is velocity changing over time you also care about the direction it also makes sense because velocity itself is a vector quantity needs magnitude and direction so the acceleration here and we're just going to assume that we're going we're going to the to the right zero miles per hour and 60 miles per hour to the right so what is that it's going to be change in velocity so let me just write it down with different notation just so you can familiarize yourself if you see it in the textbook this way so change in change in velocity this Delta symbol right just means change change in change in velocity over time over time and it's really as I've mentioned in previous videos it's really time is really a change in time but we could just write we could just write time here this three seconds is really change in time it might have been it might have been you know if you look at your second hand it might have been five seconds when it started and then it might been eight seconds when it stopped so it took a total of eight of three seconds so time is really a change in seconds but we'll just go with the time right here so we just with the T so what's our change in velocity so our final velocity is 60 miles per hour our final velocity is 60 miles per hour and our original velocity was zero miles per hour so it's 60 minus zero miles per hour miles per hour and then what is our time what is our time over here well our time is or we could even say our change in time our change in time is three seconds three seconds so this gives us 20 miles per hour per second let me write this down so this becomes this top part is 60 60 divided by three is 20 so we get 20 but then the units are a little bit strange we have miles instead of writing mph I'm going to write miles miles per hour per hour that's the same thing as mph and then we also in the denominator right over here have we also right over here in the denominator have seconds which is a little bit strange and as you'll see the units for acceleration do seem a little bit strange but if we think it through it actually might make a little bit of sense so miles per hour and then we could either put seconds like this or we could write per second per second and let's just think about what this is saying then we could get it all in two seconds or we could all get in two hours whatever we like this is saying that every second this Porsche 911 can increase its velocity by 20 miles per hour so it's acceleration is 20 miles per hour per second and actually we should include the direction because we're talking about vector quantities so this is to the east so this is East and then this is East right over here just so that we make sure that we're dealing with vectors we're giving it you're giving it a direction due east so every second it can increase in velocity by 20 miles per hour so hopefully we wait I'm saying it it makes a little bit of sense 20 miles per hour per second that's exactly what this is talking about now we could also write it like this this is the same thing as 20 miles per hours because if you if you take something and you divide it by seconds that's the same thing as multiplying it by 1 over seconds so that's miles per hour hour seconds and although this is correct to me this makes a little less intuitive sense this one literally says it every second it's increasing in velocity by 20 miles per hour 20 miles per hour increase in velocity per second so that kind of makes sense to me here it's saying 20 miles per hour seconds so once again it's not let as intuitive but we can make this so it's all in one unit of time although you don't really have to you can change this so that you get rid of maybe the hours in the denominator and the best way to get rid of an hour and the denominators by multiplying it by something that has hours in the numerator so hour and seconds and here let's the smaller unit is a second so it's 3600 seconds for every one hour or one hour is equal to 3600 seconds or one one 3600 of an hour per second all of those are legitimate ways to interpret this this thing in magenta right over here and then you multiply do a little dimensional analysis hour cancels with hour and then you have this will be equal to this will be equal to 20 over 3600 20 over 3600 miles per seconds times seconds or we could say miles let me write it this way miles for seconds times seconds or we could say miles per second I want to do that in that another color miles per second squared miles per seconds miles per second squared and we can simplify this a little bit divide the numerator and the denominator by 10 you get 2 over 360 or you could get this is the same thing as 1 over 1 over 180 miles miles per second squared per second squared I'll just abbreviate it like that and once again this doesn't make you know one 180th of a mile how much is that you might want to convert it to feet but the whole point in here is I just wanted to show you that what one how do you calculate acceleration and give you a little bit of a sense what it means and once again this right here when you have second squared and the in the bottom of your units it doesn't make a ton of sense but we can rewrite it like this up here this is 180 or 1 over 180 miles per second and then we divide by seconds again per second for a second or maybe I could write it like this per second but this is where this whole thing is the numerator so this makes a little bit more sense from an acceleration point of view 1 over 180 miles per second per second every second this Porsche 911 is going to go 101 180 of a mile per second faster and actually it's probably more intuitive to stick to the miles per hour because that's something that we have that we have a little bit of a more sense on and another way to visualize it another way to visualize it if you were look at if you were to be driving that Porsche and you were to look at the speedometer for that Porsche and if the acceleration was constant it's actually not going to be completely constant and if you looked at the speedometer let me draw it so this would be 10 20 30 40 50 60 this is probably not what the speedometer for a Porsche looks like this is probably more analogous to a a small four-cylinder cars speedometer the suspect the Porsches the speedometer goes much beyond 60 miles per hour but you what you would see for something accelerating this fast is right when you're starting the speedometer would be right there and that every second it would be 20 miles per hour faster so after a second it the speedometer would have moved after another second the speedometer would have moved this far and then after another second the speedometer would have moved that far and the entire time you would have kind of been pasted to the back of your seat

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