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Current time:0:00Total duration:13:15

Video transcript

I have some footage here one of the most exciting moments in sports history and to make it even more exciting the commentator speaking in German and I'm assuming that this is okay under fair use because I'm really using it for a math problem but I want you to watch this video and then I'll ask you a question about it tonight because so you see it's exciting in any language that you might watch it but my question to you is how fast was a sane bolt going what was his average speed when he ran that hundred meters right there and I encourage you to watch the video as many times as you need to do it and now I'll give you a little bit of time to think about it and then we will solve it so we needed to figure out how fast was a sane bolt going over the hundred meters so we're really thinking about in the case of this problem average speed or average rate and you might already be familiar with the notion that distance distance is equal to rate or speed I'll just write rate times time and I could write times like that but once we start doing algebra the traditional multiplication symbol can seem very confusing because it looks just like the variable X so instead I will write times like this so distance is equal to rate times is equal to rate times time and hopefully this makes some intuitive sense for you if your rate or your speed were 10 meters per second just as an example that's not necessarily how fast he went but if you went 10 meters per second and if you were to do that for for two seconds for two seconds seconds then it should hopefully make intuitive sense that you went 20 meters you want 10 meters per second for two seconds and it also works out mathematically ten times two is equal to 20 and then you have seconds in the denominator and seconds up here in the numerator I just wrote seconds here with an S I wrote it out there but they also cancel out and you're just left with the you the units of meters so you're just left with 20 meters so hopefully this makes intuitive sense with that out of the way let's actually think about let's actually think about the problem the problem at hand what information do we actually have so we do we have the distance so what is what is the distance in the video we just did and I'll give you a second or two to think about it well this race was the hundred meters so the distance was 100 100 meters now what else do we know do we know well we're trying to figure out the rate that's what we're going to figure out what else do we know out of out of this expression out of this equation right over here well do we know the time do we know the time what was the time that it took hussein volt to run the hundred meters and i'll give you another few seconds to think about that well luckily they were at timing the whole thing and it not and they also show that it's a it's a world record but this right over here is in seconds it's how long it took a sane bolt to run the hundred meters it was nine point five eight nine point five eight seconds and I'll just write s four seconds so given this information here what you need to attempt to do is now give us our rate in terms of meters per second I want to think if you can figure out the rate in terms of meters per second we know the distance and we know the time well let's substitute these values into this equation right over here we know the distance is 100 meters the distance is 100 meters and it's equal to we don't know the rate so I'll just write rate right over here it's C again let me write in that same color it's equal to rate rate times and what's the time we do know the time it's nine point five eight seconds nine point five eight nine point five eight seconds and we care about rate we care about solving for rate so how can we do that well if you look at this right-hand side of the equation I have nine point five eight seconds times rate if I were able to divide this right-hand side by nine point five eight seconds I'll just have rate on the right-hand side and that's what I want to solve for so you say well wait we won and I just divide the right-hand side by nine point five eight seconds nine point five eight seconds because if I did that the nine that if the unit's cancel out if we're doing dimensional analysis don't worry too much of that where it doesn't make sense to you but the unit's cancel out and the nine point five eight cancel out but I can't just divide one side an equation by a number when we started off this is equal to this up here if I divide it if I divide the right side by nine point five eight in order for the Equality to still be true I need to divide the left side by the same thing so I can't just divide the right side I have to divide the left side in order for the Equality to still be true if I said one thing is equal to another thing and I divide the other thing by something in order for them to still be equal I have to divide the first thing by the same amount so I divide by nine point five eight seconds so on our right hand side and this was the whole point these two cancel out and then on the left hand side I'm left with a hundred divided by nine point five eight and my units are meters per second which are the exact units that I want for rate or for speed and so let's get the calculator out to divide 100 by nine point five eight so I've got 100 meters divided by nine point five eight seconds it gives me ten point let's say we get a little about three significant digits here so let's say ten point four so this gives us ten point four and I'll write in the rate color ten ten point four and the units are meters per second meters meters per second is equal to is equal to my rate now the next question so we got this in meters per second but unfortunately meters per second is they're not the you know when we drive a car we don't see the the speedometer in meters per second we see the either kilometers per hour or miles per hour so the next task I have for you is to express this speed or this rate and this is his average speed or his average rate or the hundred meters but to think about this in terms of kilometers per hour kilometers per hour so try to figure out if you can if you can rewrite this in kilometers per hour well let's just take this step by step so I'm going to write so let me just go down here start over so I'm just I started off with ten point four and I'll write meters in blue meters in blue and seconds seconds in magenta now we want to get the km/h right nowwhat m/s so let's take baby steps let's first think about it in terms of kilometers per second and I'll give you a second to think about what we would do to this to turn this into kilometers per second well the intuition here if I'm going ten point four meters per second how many how many kilometers is ten point four meters well a kilometers is a much larger unit of measurement it's a thousand times larger so ten point four meters will be a much smaller number of kilometers and in particular I'm going to divide by a thousand another way to think about it if you want to focus on the units we want to get rid of this meters and we want a kilometers so we want a kilometers and we want to get rid of these meters so if we had a meters in the numerator we could divide by meters here and they would cancel out but the intuitive way to think about it is we're going from a smaller unit meters to a larger unit kilometers so 10.4 meters are going to be a much smaller number of kilometers but if we look at it this way how many how many meters are in one kilometer one kilometer is equal to one thousand meters this right over here one kilometer over a thousand meters is over one over one we're scent we're not changing the fundamental value we're essentially just multiplying it by one but when we do this when we do this what do we get well the meters cancel out we're left with kilometers and seconds and the numbers you get ten point four divided by a thousand ten point four divided by a thousand is going to give you so if you divide by ten you're going to get one point zero four you divide by 100 you get point one zero four you divide by a thousand you get zero point zero one zero four so that's just ten point four divided by a thousand and then our units are kilometers kilometers per second so that's the kilometers and then I have my seconds right over here now so let me write the equal sign now let's try to convert this to kilometers per hour and I'll give you a little bit of time to think about that one well hours there's there's 3,600 seconds in an hour so how for many kilometers I do in a second I'm going to do 3,600 times that in an hour and the unit's will also work out if I'm going I'm right now well if I do this many in a second so it's going to be times 3,600 there are 3,600 seconds in an hour 3,600 seconds in an hour and another way to think about it is we want hours in the denominator we had seconds so if we multiply by seconds per hour there are 3,600 seconds per hour the seconds are going to cancel out and we're going to be left with hours in the denominator so seconds cancel out and we're left with kilometers per hour but now we have to multiply this number times 3,600 I'll get the calculator out for that I'll get the calculator out for that so we have we have point zero one zero for point zero one zero for times 3,600 3,600 gives us 37 point I'll just say 37 point four so this is equal to thirty seven point four thirty seven point four kilometers in la me ters km/h km/h so that's his average speed in kilometers per hour and now the last thing I want to do for those of you for those of us in America will convert into imperial units or sometimes called English units which are ironically not necessarily used in UK they tend to be used in America so let's convert this into miles per hour and the one thing I will tell you just in case you don't know is that they're 1.6 one kilometers is equal to 1 is equal to one mile so I'll give you a little bit of time to convert this into miles per hour well as you see from this a mile is a slightly larger or reasonably larger unit than a kilometer so if you're going 37.4 kilometers and a certain amount of time you're going to go a slightly smaller amount of miles in a certain amount of time or in particular you're going to divide by one point six one so let me rewrite it if I have 37.4 km/h kilometers per hour we're going to a larger unit we're going to miles so we're going to divide by something larger than one so we have one we have one let me write it in blue one mile one mile is equal to is equal to one point six one kilometers or you could say there's one one point six one mile per kilometer and also once again works out with units we want to get rid of the kilometers in the numerator so we would want it in the denominator and we want a mile in the numerator so that's what we have a mile in the numerator here so let's once again multiply or I guess in this case we're dividing by one point six one and we get so we get let's just divide our previous value by one point six one one point six one and we get twenty three point I'll just round up twenty three point three this is equal to twenty three point three twenty twenty three twenty three point three and then we have miles miles miles per hour 20 miles per hour which is obviously very fast he's the fastest human but it's not maybe as fast as you might have imagined you know in a car twenty three point three miles per hour doesn't seem so fast and especially relative to the animal world it's not particularly noteworthy this is actually slightly slower than a charging elephant so charging elephants have been clocked at 25 miles per hour