foreign hi this is Mr Anderson and today I'm going to be talking about speed velocity and acceleration if you've ever seen Usain Bolt run from Jamaica well first of all it's highly impressive uh but you have an understanding of how fast fast really is um in physics we deal with really just two of these in other words speed is a scalar quantity and you've and if you speed your whole life you say my car can go 20 miles an hour or my car can go 200 miles an hour and we're talking about speed it's a scalar quantity and if you don't really know what a scalar quantity is make sure you watch the video on that but velocity and acceleration are vector quantities and so they include not only how the magnitude but also the direction at which uh velocity or or position might be changing over time and so in this video I'm going to show you how to do some simple problems with velocity acceleration kind of explain what it is but we'll get into a lot more detail when we look you through position versus time and velocity versus time graphs eventually um so let's get going before I get started however there is a little cheat that I want to remind you and that's because I live in the U.S and since I live in the U.S I really have a hard time dealing just in my brain with meters per second and so if you do any problem in physics you always have to use the units meters per second but in the back of my head I have this in other words if I say something's going 10 meters per second in the back of my brain I have to think oh that's about 22 miles an hour because that gives me an idea of really how fast something is going so if you want to use that in the back of your head you can but don't use it in your equations or you're going to get the wrong answer now velocity is a vector and what does that mean when you're ever talking about velocity you have to say not only let's say 2.6 meters per second but you have to give me the direction that that's moving in so it could be North or could be West or it could be up or it could be down and so if you ever give a velocity make sure you have the direction now you're going to find immediately in this video that I quit talking about Direction and so you may think he just told me directions important but now he doesn't even use Direction and the reason why is that we generally use a coordinate system like this and so if an object is moving up we'll say then it's going to have a positive velocity and so that positive actually tells me the direction it's moving in or if it's not sitting on something and gravity pulls it down then it's going to move in the negative direction we're in the problems today Usain Bolt I'm going to assume is starting at the origin and then he's running in the positive direction but if the wind came up a real big wind and Bloom in the opposite direction then he'd be moving in the negative and so I'm not cheating I'm actually including positive and negatives to uh to explain that also that you should understand the difference between an average and an instantaneous velocity um and average velocity is looking at a certain period of time and saying how fast did it move during that period of time but along that race of Usain Bolt he has all these different instantaneous velocities that are a little bit different and the best way to explain that is maybe with some videos that I just shot so let me bring up one of these uh this is a video of me let's see go back to the beginning so this is me taking a weight and then just dropping the weight so what I can do let me go back for just a second if I go right here and I think I should be able to draw on this so what I can do is I can actually Mark where that weight is so let's go back a second so right here the bottom of the weight will say is right there and now it drops a frame in the bottom of the weight is right there and it drops a frame and the bottom of the weight is right there and now it's right there and that was a way down here and so what we can look at is that this is an object that is changing in velocity and so its velocity way up here was actually zero and then its velocity change and it got faster and faster in the negative Direction over time uh and so that would be an instantaneous velocity wherever it is but I could also take this whole thing and figure out what's the average velocity over that and so make sure you kind of understand the difference between the two let's try another one of these here's another one video I just made so this is just an object that's rolling across the table so let's get that back again so I'm going to give it an initial push thank you so I give it an initial push and then according to Newton's Laws an object in motion tends to stay in motion and so I'm going to Mark the middle of the object right here it's going a little slower and so let's go a couple one two three frames and now it's right here one two three frames and now it's right here one two three one two three one two three two three one two three two three okay and so I gave that an initial velocity and if you look at it it seems to be uniform and so in this case we'd actually have an instantaneous velocity at any one point that's actually equal to this average velocity over the whole distance and when we get to doing some some graphing that that'll make a little bit more sense but remember there's a difference between the two and so I kind of will use them interchangeably but make sure you understand which of the ones I'm I'm talking about okay so definition time if you need to solve some problems this is the definition for velocity so definition of velocity it's simply change in X over the change in t where X is its position and T is equal to the time and so to solve a problem that you might have like on a worksheet or a test let's do Usain Bolt so his world record in the hundred point meter dash is 9.58 seconds and so to figure out his velocity this is how it works in my brain I go Delta X over delta T So Delta X is simply the change in X over the change in T and so how far does his distance change well it's going to be 100 Point meters always make sure you're including the correct number of significant digits and the units as well otherwise you're going to get stupid answers now we look at the change in time well the change in time is 9.58 seconds okay so how do we do this we're going to divide 100 Point meters divided by 9.58 seconds I did that just a second ago and I got 10.4 and the and the units then are going to be in meters per second and so the average velocity of the same bolt during this whole run is 10.4 meters per second using that brain trick again if I take that times 2.2 he's going roughly uh 23 miles per hour to give you an idea of what is average speed is and so that'd be a pretty simple velocity kind of problem sometimes it doesn't start from rest in other words it doesn't start from a time being zero and a velocity being zero as well and so a better way to remember what velocity is instead of the change in X over the change in T is It's the final X or its final position minus its initial and so get used to this in science the F always stands for final and the I always stands for initial divided by the final time minus the initial time and so this is a better way to explain what velocity is and let's try a problem where it where it actually varies a little bit these are the splits from the um Usain bolts race this is actually in the Olympic record where he ran 9.69 and so the first thing let's do is let's try to figure out the velocity for the first meters first 10 meters and so velocity remember is going to be x f minus x i where XF is the final position and then it's going to be TF minus t i okay and when you when you ever solve problems you want to make sure you identify what do I know well what's the final position that's going to be 10.0 so 10.0 what was his initial position and again I should put meters what was his initial position that was zero so that's minus zero what was his final time that'd be 1.85 1.85 and then what was the initial in seconds it's zero seconds so what I get here is well roughly 10.0 meters over 1.85 seconds and so when I work this earlier and I get 5.41 so it'd be 5.41 meters per second now why does this have three significant digits because that has three and that has three as well um so how fast is that in miles per hour it's not very fast I don't know like what 13 14 miles an hour um let's look how fast he's running later in the race though and let's so let's try it way down here so if we go way down here let's say at this point so remember uh velocity is going to be final x minus initial X over time final minus time initial and this is why you'll start to see why it's important that we that we kind of keep track of that so which during this next 10 meters he ends up at 70.0 meters uh and he started at 60.0 meters so this would be the initial distance the final time is 7.14 seconds and the initial time is 6.32 seconds so what does that equal well that equals 10.0 meters divided by 0.82 seconds and so the right answer should be 12.2 meters per second so that'd be the right answer with three significant digits I'm doing that uh into miles per hour it's around 27 miles an hour so it's a ridiculous amount of speed and so this would be his speed down here 12.2 meters per second and remember when we were way up here speed was only 5.4 meters per second and so what has happened from here to here well the velocity is actually increased and so you know what that means what does it mean when your velocity is increasing that means that we're accelerating and so not only is the velocity important but what happens to the velocity over time is also important and so that's what acceleration is acceleration is the change in velocity over the change in time and you'll feel look the equation is very similar we take the final velocity minus the initial and then divide that by the final time divided by the initial time now the units are a little bit weird if you think about it we're taking meters per second which is what the velocity is measured in and we're dividing it by a second and so lots of times we'll just write that as meters per second squared now what's one acceleration that you should learn this is the acceleration due to gravity so the acceleration due to gravity is negative 9.8 meters per second squared what does that mean if we take a person like this standing at the top of a cliff and they fall off um at the at zero seconds they're going to be going 9.8 meters per second excuse me at the top they're going to be going zero meters per second but after one second they're going to be going 9.8 meters per second so if you jump off a cliff after one second you're roughly going 23 miles an hour after two seconds you're going 46 miles an hour after three seconds you're going you know 68 whatever miles per hour and so you're going to go really really fast very quickly and so that's acceleration due to gravity why it's in the negative is that remember on our coordinate system this would be in the positive and so this is going to be in the negative as we go down let's try an actual problem uh to to how you would have to solve a problem like this this is the Bugatti Veyron which is made by Volkswagen and it's the fastest production car um that you could buy which if you had a bunch of money it goes like 250 miles an hour and so let's try to do an acceleration programs uh problem so acceleration remember is the change in velocity over the change in time so let's figure out if it can go from 0 to 60 and 2.46 seconds what kind of an acceleration are we talking about so again that's going to be VF minus v i over TF minus t i so what's our final velocity our final velocity is going to be 60 miles an hour which we couldn't use in an equation we have to convert that to meters per second so that'd be 26.9 meters per second minus 0 because it starts at a stand still what is its final time its final time is going to be 2.46 seconds minus zero seconds because it goes from a standstill and so now we can figure out the acceleration so 26.9 divided by 2.46 is going to be 10 .9 meters per second squared so that'd be the right answer so going back again figuring out what the acceleration due to gravity is if you're falling off a cliff you're going to experience an acceleration in the negative or down of 9.8 meters per second if you're sitting in this car you're actually going to feel more acceleration than you would falling off of Cliff as you accelerate and so I don't know what that's like but I bet it feels really really cool and so I hope that's helpful