hey, gang, let's suppose it's joke-telling time right now. i'm gonna tell some jokes. you ever be at a party and it's joke-telling time and it's your turn to tell a joke and you say to yourself, "hey, wow, i remember a joke, darn it, but darn it, no, i don't remember it." you don't have it. what jokes is it that you can tell when it's joke-telling time? jokes that you've heard before or jokes that you've told before? what is it? isn't it jokes that you've told before? so if you want to become a good joke-teller, you know what the best thing to do is? is when you hear a joke, find a friend and tell the joke right away and tell the friend the joke, then it's yours. and tell another friend. if you tell a joke three times, that's your joke, and that's a joke you'll always remember. so you know what i'm gonna do in this course a lot? i'm gonna ask you to check with your neighbor and talk about the ideas of physics because my feeling, that if you talk about these ideas, they'll become a part of you, and that's what we want, the ideas of physics to become us. yeah? so we'll be doing that a lot.

check your neighbor in time. all right. let's begin. let's start off with this question: what--we're talking about motion today. chapter two: motion. what mode of transportation has done more to change the way people live? think about that and check with your neighbor. begins with an e-l, end with vator. [laughter] elevator. isn't that right? elevator. high-rises. could you imagine living on the 32nd floor and having all stairs? so the fact that the elevator came along changed the way cities are built. now, we go straight up, huh? high-rises. we're gonna talk about motion today. we're gonna talk about a lot of definitions. first definition for motion is how fast you move. that's speed. so speed. we defined speed to be-- speed is measured in, like, miles per hour, so it's distance compared to time. so speed is simply distance compared to time.

if i travel 60 miles and i do it in a time of 1 hour, what's my overall speed? 60 miles per hour. try it. 60 miles an hour. 60 miles an hour. okay? let's suppose i go 70 miles in 1 hour. what's my speed? 70 miles per hour. 70 miles per hour. let's suppose i go 100 miles and it takes me 2 hours. what's my speed? 50 miles per hour. 100 miles for 2 hours or 50 miles per hour. right? can you do metric units? let's suppose i go 60 kilometers and it takes me 1 hour. what's my speed? what is it, gang? 60 kilometers per hour. okay? so speed is simply distance over time. we make a distinction between speed and velocity. not gonna knock you to death, but the idea is this: to say that you know your velocity is to say you know something else

besides how fast you go. you know what it is? direction. which direction you go. like an airplane pilot says, "my velocity is so many kilometers per hour north." speed plus direction. so to say something is moving with a constant velocity is to say something is moving with a speedometer reading staying the same but also the compass reading staying the same. so velocity is speed but with direction implied or specified. so the symbol for speed will be the symbol for velocity, and it's v. v, velocity. so i can put this in shorthand notation and come up with our first little equation. and that's v equals d, for distance, divided by time. this is a shorthand way of saying this. it's simply a definition of speed. given the distance you travel, given the time interval during which that distance is traveled, the ratio, quick boom, that's your speeeed.

your distance--your ratio of distance to time may change. sometimes, you might cover a lot of distance in a short time, and other times a longer distance in a longer time, so it may change. so strictly speaking, we say your average speed is how far you go divided by how long the time it takes. i put that little bar there to mean average, average speed. knowing that, we can turn around and say this: if i tell you that my average speed is 60 kilometers per hour and i travel in a half hour, can you tell me how far i've gone? check your neighbor. see if your neighbor be knowing. what's the answer, gang? 30 kilometers. 30 kilometers. how did you get it? 60-- you can turn this around. if this is true, then the distance you travel is simply equal to the average speed multiplied by the time you travel. and so this, a relationship for how far, and this, a relationship for how fast,

at least the average of how fast. your average speed and the distance you travel and you know the average speed and the time of travel. let's try it one more time. let's suppose you're in an airplane. the airplane is going 600 kilometers per hour, and it does it for 2 hours. how far along will the airplane have traveled? neighbor time. 600-- 600 kilometers per hour and it does it for 2 hours. try it. you would say 600 kilometers per hour multiplied by 2 hours is 1,200 kilometers. so the airplane ought to be 1,200 kilometers distant from where we started. questions? okay. now we're gonna talk about an idea that is considerably more involved, a little more difficult. and it's not how fast, and it's not how far. it's the rate at which you change how fast. and that's acceleration. let me just define it.

acceleration equals a change in speed, a change in velocity, a change in motion. the key word: change. over some time interval, which i do note as t. if a system moves and changes how it moves, then that system is accelerating. let me give you an example. you're standing at the racetrack, you and your friends, and you're seeing the cars scream by, screeching rubber, okay? [makes sounds] 200 miles an hour here, 200 miles an hour there, 200--just 200 miles an hour screaming, rolling. and your friend says, "wow, man, you see those cars accelerate?" and you say, "as a matter of fact, i didn't." your friends, "what, 200 miles an hour, man, come on." 200 there, 200 there, 200 there, 200 there, what's the change?

no change. if there's no change, then there's no acceleration. i'll give you an example over here. here i have a piece of metal. i'm gonna push the metal at constant speed. what's the acceleration? none. begin with a z. zero. end with a p. zip. [laughter] no acceleration, see. it's moving without accelerating. okay? it has speed. it has velocity. now, when i get it started, i have to-- when i get it started, it accelerates briefly, but then it just moves uniformly. no change in motion. so it moves without accelerating. a lot of people don't know that. a lot of people think that if something is not accelerating, it got to be at rest. but what do we know? no, no, no, no, no. it's just moving without change. you see the difference there?

so acceleration means there must be a change. and i can put this is in shorthand notation. say--like that. and i can give you a numerical example. let's suppose you're buying a car and someone says, "hey, this car is really, really neat. "it doesn't look very nice, kind of a little bit tacky, "but this thing will accelerate-- this car will go from zero to 60." what's the person telling you? zero to 60. zero to 60 miles an hour, does that tell you anything? then you buy the car, and you find out it takes you half an hour to get up to 60 miles an hour, okay? [laughter] so when you're talking about acceleration, you're talking about how long does it take to do that? well, let me give you an example. if i have a car that go from zero to 60 miles an hour in 10 seconds, what's the acceleration? try it. let me help you.

the car is gonna change its velocity by how much? from zero to 60 miles an hour, okay? so there's gonna be a change in velocity of 60 miles an hour. right? did i tell you how long it would take to do that? 10 seconds. 10 seconds. so i'll divide that by 10 seconds. s for second. so you know what the acceleration of my car is? anyone have a calculator? maybe you can do it in your head? okay. you can, okay? it's gonna be six miles per hour per second. so the acceleration of that car is six miles per hour per second. and if that acceleration stays uniform, stays constant, that's to say then as long as it's doing that, every second goes by, the car is going to go be going faster than the second before. by how much? six miles per hour. by six miles per hour. you'll gain six miles per hour every second. ain't that neat? so that's the acceleration of the car. let's suppose i told you this: i have a car that will go from zero

to 100 kilometers per hour in 10 seconds. what's the acceleration? from zero to 100 kilometers per hour in 10 seconds. let's see if you can do it at your desk. go. in this case, you're going 100 kilometers per hour and changing to 100 in 10 seconds, and so what do you have over here? 10. 10... kilometers. ...kilometers per hour per second. okay? you get the idea? acceleration is something that you can feel. when you're in a car and accelerate, you can feel that acceleration. in fact, you have controls in the car that make the car accelerate. what are the controls? what's the most obvious control in your car that will make it accelerate? the accelerator. the accelerator. okay? and your accelerator is your gas pedal, right? physics-types, all right? your gas pedal. because when you push down on the gas pedal, it accelerates your car. it changes how it moves. you're driving along steady, steady, steady. you wanna pick up speed, you step on the gas. you--woop. okay? and you feel that lurch. you can feel the effect of acceleration. is there any other controls on the car

that will make it change how it's moving? beginning with a b, end with rake. try it. brake. your brake. and when you slam on the brake, what happens? poom. everyone pitches forward. you can feel it. because there's a change. you can feel that change. is there another control in your car that will make it accelerate? the steering wheel. steering wheel. that's right. you're driving on the road and you take that steering wheel, you go like this. woop. everyone on the car lurches to the side. you can feel the effect of acceleration. interestingly enough, if you're moving at steady speed with no acceleration, not only can you not feel that you're moving, you really have no proof that you're moving at all. let's suppose you're in an airplane, the pilot's at 600 miles an hour, but you look out and everything seems to be at rest. you take a coin, you flip it. it behaves just the same way as if you're at rest. all the little devices you can put on board, there's nothing you can do to tell whether you're even moving. you look out, you see the ground going by. maybe from the stars, you look down, you see--you standing there

and the ground's going like this. so that brings up a whole new idea. that motion is relative. when we say you're moving 60 miles an hour, we mean 60 miles an hour relative to, with respect to maybe the ground, usually, the earth. but motion is always relative. and we're just saying this. if you're moving at constant motion, no change, then you can't even tell whether you're moving. and the person who can come up with an experiment to detect that will probably be given the nobel prize. 'cause it's one of the things in physics we cannot detect uniform motion. we can't say for sure. no way to sense it. we only sense changes in motion. take a cup of tea in that airplane. when the airplane starts to do something different, the tea will spill. okay? but if you're moving steady, steady, steady, steady, look out, you see the trees go by. but at the end, how do you know it's not you at rest and the tree is moving? there's no experiment that will discern uniform motion.

take a piece of clay and drop it. did it accelerate? yeah. how do you know? how do you know? because you saw it change. you saw it up here at rest. did you see it gain speed? let me try it from up here. can you guys see it gain speed when i drop it? did you see it pick up speed? very difficult to tell, but you know it does pick up speed. you know that intuitively because if i took this clay and i hold it above and i say, "would you dare to catch this?" dare to? yeah. yeah. you dare to catch it? okay. now, we're gonna do the same thing. i'm gonna go out on an airplane and i'm gonna drop it. and you catch it. would you dare to catch it? oh, no way. because you know as this thing is falling, it's gonna pick up speed. isn't that right? and to say it picks up speed is to say it's gonna be undergoing a process begin with a called...

acceleration. acceleration. okay? and that pick up in speed, that's what acceleration is. and i'm just--we just saw here this thing does accelerate. let me tell you how much it accelerates. it turns out that a freely falling object at the surface of the earth will have a constant acceleration, and that acceleration will be 10 meters per second every one second. freely falling objects will pick up a speed of 10 meters per second every second they're falling. and i can call that like this: 10 meters per second square. when the acceleration is due to gravity, it's common to let the a be a g. you can say g for the planet earth is 10 meters per second per second, or 10 meters per second square. what's that mean? that means this.

let's suppose i drop this-- okay-- and there's a speedometer on there. and you guys are looking at the speedometer with a spyglass. right now, what does the speedometer say? zero. zero. now, when i let it go. does the speedometer reading pick up? yes. it picks up. at the end of one second, the speedometer reading gets up to how much? 10. 10, that's right. because it was falling for a whole second. so now, it's going 10 meters per second, okay? one more second, it's going even faster. how much one more second? 10. 10. now, it's up to 20. right. yes. and the--up to the third second, it picks up another value of how much per second? 10. 10, so how fast is it going then at three seconds? 30. how about four seconds. 40. can you do big numbers? [laughter] how about 10 seconds? 1,000. how fast is it going? check your neighbor. okay? not okay. not the 10. let's just say seven. -- 70 meters per second. can you do nines? [laughter] how about nines and sevens now?

i can never do nines and sevens, okay? but 10 is easy, right? 100 meters per second. so that brings us up to another formula. if that's what acceleration is, we can tell how fast things go by just saying this: the velocity-- you know, the velocity acquired when falling is simply equal to the acceleration times the time. and if the acceleration for free fall is always 10, then the speed something picks up is simply gonna be 10 multiplied by that time t. that's what we just did. i asked you people--i says, "if you go for 10 seconds fall-- fall for 10 seconds, how fast is it going?" where the t is, you put 10. and that cancels out one of these seconds over here, and so what you're left with is 10 10s is 100 meters per second. so a freely falling object will pick up to a speed

of 100 meters per second if it's got 10 seconds to fall. how about if it's got five seconds to fall? how fast will it be going? what would the speedometer reading be? check your neighbor. how many say 50 meters per second? yeah. because every second it goes by, it's gonna pick up 10 meters per second it didn't have the second before. and that acceleration is constant. and you know what we're doing, gang? we're forgetting about air drag. we're not gonna count air drag. if i take this book and this piece of paper and drop them-- the book accelerates much more than the paper. why? because the paper, there's a lot of air resistance compared to the weight of the paper. if i take that paper and make it smaller, so now the air resistance acting on is not gonna be so much, they'll fall together. okay? and we're only taking the case-- these are-- these relationships here, these are for the case where air resistance doesn't count. and we're gonna kind of do things that way in this course. we're gonna take the easiest way all the time.

you know why? because the easiest way is a lot. we're not gonna complicate things by talking about the air drag. at least, not at this point. or even the buoyancy, the amount of air that's displaced and all that. we're gonna learn the simplest physics we can, and we're gonna learn it well. and then we learn that well, then maybe some other time, you can put air drag and buoyancy and all those other things in and make it more complicated. we'll always take the easiest way and learn a lot. better to uncover a little than to cover a lot. now, i got a question for you, gang. let's make believe this is a little test. i suppose we get up here again and take the object and i drop it. make believe this is a quiz. and i drop it. peewww. one second later, i say stop. one second later, that thing has got speed it didn't have up here. check your neighbor and see if your neighbor knows how much speed does it have after one second.

go ahead. it's a review. how many said 10? show of hands. look at the hands that aren't up. okay. so let me tell you how we got the 10, gang, okay? when you drop something, it's gonna keep going faster and faster. how much is it gonna go faster every second? 10 meters. 10 meters per second. all right. every second. and we said one second, so the answer is-- begin with a t. 10. 10. that's how fast it's going, right? let's suppose i had dropped it for a longer time and it took two seconds? i said two seconds later, what's it speed? and you would say? 20-- if i said seven seconds even, you would say? 70. okay? now, i'm gonna ask another question. i take it. i drop it. peewww. one second. one second later, how fast is it going? 10. how far has it fallen? 10 meters. one meter. ah. 10 meters. i switched. i asked: how far?

yeah. yeah. 10 meters. i didn't ask: how fast? how fast is 10? how far is not revealed. how far brings up a new idea. how about it, gang? how far? how many say 10? how many say five? how many say i don't know? how many say i only don't know, i don't need to know, i don't care? [laughter] okay, come on. let's look at it, gang. let's look at it. you say 10. did it have an average speed of 10? see, it fell for one second, but its average speed wasn't 10. if you take a couple of quizzes and the first quiz you take is zero and the next quiz you take is 10 and someone says, "how do you do in physics?" "oh, i'm not bragging an average of 10." no, you--average of 10. what's your average if you get a zero and a 10? five. five. in the middle, huh?

so when i started, the thing wasn't moving at all. one second later, it's going 10, but the average then is five. so the average speed of five meters per second over that one second gives you a distance of five meters. so it's only gonna fall five meters, gang. and we can do that for any number of meters if we just do it in general. say, like this. the average speed when acceleration is constant, it is simply the speed you begin with plus the speed you end up with divided by two, the average amount, and then multiplied by the time of fall. but we're always gonna take the case where the initial speed is zero. so we're simply gonna end up with the speed we end up with at the end of any time interval divided by two multiplied by the time. what's the speed that an object will have after it's fallen, just in general?

for one second we know it's 10, but how about t seconds? anyone know? do we have any relationship for how fast something falls? right here. in fact, if the acceleration is g, the speed is gonna be gt, the one we had right over here, huh? so let's put that over here. see what we have here? is this time and this time the same? this is the time that it was falling. and this is the time it was falling too. they're the same time. so i can say i can make this a little bit more shorten up.

and now, i have a relationship for how far something falls. over here i have how fast. and let's say for fall let "a" be g, let 10 meters per second per second. later on, you're gonna learn that the 10 meters per second per second is more probably 9.8 meters per second per second, but 9.8/10, same same. you can see the idea better with the 10 rounded off. you're on the mainland. you're up country, my country, california. you're out with your friends.

and you know friends there and someone opens up an old mine shaft, musty. someone says, "geez, i wonder how deep that is down there." dark, dank, you can hear the bats, straight down. someone says, "gee, i don't know. "if we had a rope we could lower the rope and find out when it hits the bottom." --the ladders all broken, i don't think-- there's no way to find out how far down that goes. and you say, "wait a minute, hand me that rock." your friend hands you the rock, you take the rock. [makes sound] five. five seconds it takes to hit the ground. disregarding the time it takes for the sound to come back up, it took five seconds to hit the ground, right? someone says, "well, how deep is it?" and you say 5 seconds, 5, 5, 25, 25 times 5, "it's about 125 meters deep." some say, "how did you know that?"

and you say, "college." [laughter] do you see that? do you see you can tell how deep it is? all you got to know is the time it takes to drop. multiply that time by itself, and then multiply that by half a g. if g is always 10, we can just say here, without putting units in there. we can also say that speed equals 10t. if you understand these ideas, if you really do, you can answer these questions. this is like a quiz. i take my object, i drop it. it takes 3 seconds, 3 seconds to hit the ground. question number one, what's the speed of impact? what's the speed of impact, it takes three seconds to hit?

what's the speed at which it felts against the ground? see if you can write that down in your notes. so what's the speed gonna be, gang? 30 meters per second. that thing, you know, fell into the ground at 30 meters per second. now, i'm gonna ask another question. how far down did it fall during that three seconds? you gotta figure that out. see if you can do it, and then check your neighbor. how many say more than 40 meters? how many say less than 50 meters? how many say give us 45 meters anyhow. okay? 45 meters, that's right. okay. here's for the ace students. i drop it. [makes sound] three seconds it hits. a split second, a split second just before it hits. boom, at that instant, what is the acceleration? check your neighbor. how many say 30? how many say something less than 30?

how many say zero? how many say 10? hands up, higher, everyone look at these hands that are up. see these people with their hands up, make friends with those people, all right? [laughter] they're physics types. the acceleration stays 10, gang, all the way down it stays 10. you see that? the acceleration doesn't change. later on, we'll learn the acceleration will change only if the force acting on it changes. and it's falling because of the force of gravity. and that force stays the same all the way down. so the acceleration stays the same. and because the acceleration stays the same, the speed keeps getting more and more. okay? if i threw it up, it would go against the acceleration speed you're getting less and less. see? but we'll just hold the rate at which this change takes place and that's that 10 meters per second per second. so the answers again are 30 meters per second, speed; 45 meters distance travelled, but 10 meters per second per second acceleration.

got the difference there? let me ask you this question. if i take a rock and i throw it up in air, straight up, and i-- it leaves my hand at 10 meters per second, that's about a little more than 20 miles an hour. it leaves my hand at 10 meters per second going straight up. there are people who can calculate how long it'll be in the air. there are people that can calculate how high it will go. and then there are people that can't calculate these things. some of those people that can calculate these things are sitting right here today. let me ask you guys a question. how long is it gonna take to get to the tippity top if it leaves my hand at 10 meters per second? reasoning goes like this, when i drop it, it's gonna gain speed, 10 meters per second every second, right? well, just take a little savvy here now. if it gains going down, what is suppose that does going up? well, it will still gain, keep going faster and faster. come on, come on. [laughter] you guys know, it's gonna slow down. and what's the rate of slow down?

10 meters per second every second. but you threw it at 10, and you know it's finally gonna go stop to zero, yeah? so how long the time it gonna take for that to happen? begin with a w. one. one. okay. [laughter] now, if it takes one to get up, how long to get back down? one. so what's the total time? begin with a-- [laughter] two. so it's gonna be two seconds, one second up and one second down. ain't that neat, huh? how fast it gonna hit? if you throw it here at 10, how fast you catch it? 10. 10. 'cause what slowed it down going up, speeds it up coming down. and what's the rate of change of motion? 10 meters per second every second. ain't that neat? now, if you're on to that, you can do this one. well, suppose i threw baseball up in the air, and i threw it at 30 meters per second. 30, that's fast.

30 meters per second, how long is that gonna be going up? well, how many 10s do you got in 30, honey? you got three of them, right? you get the idea? every second that goes by it's gonna lose 10. so you get 10, 10, 10, 3 seconds to get to the top. how many seconds to get back down? three. what's the total time? six. six. how fast it gonna hit? 30. 30, see, the speed it lose going up, the speed it gained coming down. all right, isn't that neat? it has to go straight up, man. now, here's the question for you. when i throw it up at 30 meters per second, right at the tippity top, right at that split second, what's its acceleration? zero. zero. zero. think about that, okay, next time, physics.

and hey, hey, wait a minute. i want you to think about something else, too. air resistance, i'm gonna take a piece of paper and drop it with this book, okay. i drop the book and the paper, which gonna hit the ground first? which gonna have the greater acceleration gain, huh? which? it turns out the book because of air resistance. is it because the book's more massive? no, because i can take the paper and go like this. which accelerates more? same, same. so the air resistance is a factor. here's something i want you to try at home. take a piece of paper and hold it underneath a book, all right? now, which will have the greater acceleration, the paper or the book? same, same. i want you to try this at home. put the paper on top of the book, yeah, and now drop. which will have the greater acceleration? so you have two questions about acceleration to think of. what's the acceleration at the top, when i throw an object, and which has the greater acceleration when i drop these two? those are physics, gang, one to think to about

and the other to do. all right? catch you next time, physics, yay, all right? [music]

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