Introduction to motion - part 2 Video

Get it off your chest – be the first to comment on this video!

Introduction to motion - part 2

Introduction to motion - part 2 All right, so where I left off in the last presentation I was dropping penny from the top of a building. Once again you should not do because you can kill somebody. So, let’s say I have here, here’s the building, here’s the bad person who’s going to drop something. And let’s say they just hold it out and it just drops, the penny drops. So, the penny is going to accelerate at the rate of gravity, so it’s going to accelerate at 10m/s2. So, let’s start with an interesting question. After 2sec, so, when T=― and let’s say they drop at right T=0. So after 2sec, after 2sec, how fast is it going? So, time is equal to 2sec or we can even say this changing we are assuming that we are starting a time equals zero, so time and changing is the same thing. If time is equal to two seconds how fast is going to be going after three seconds. Well,, let’s use that formula, velocity is equal to acceleration, Well, acceleration is the acceleration of gravity, so, that’s 10m/s2, velocity Well, be 10m/s2 times time, times two second, times two second, two seconds. Well, we can just, velocity, we can multiply the numbers, we got 20 and then just like the numbers you can treat the units almost like variables the seconds is the same thing as S, right? So, this S is going to be the numerator and you have S2 in the denominator. So the S, at least this S Well, cancel out with one of the two Ss’ and I multiply down here. So I Well, up with― Well, actually let me right down― it Well, be 10m/s2 and that’s the same thing as 20, that cancels out and this may set one, so that equals 20m/s. So, you starting get a little of intuition why acceleration units are m/s2. So after two seconds we’re going 20m/s. Now let me ask you a slightly more difficult problem that not might be obvious to you. After two seconds, how far has the penny gone? Well, this is interesting. We have this formula here, distance is equal to velocity times time. But the velocity is changing the entire time, we know after two seconds the velocity is 20m/s, so we could call this the final velocity, so let’s just call that V sub F, that’s just a fancy way of saying final velocity. But, right when we start at T equals zero what was the velocity. Well, right when I started the initial velocity V sub for initial is equal to 0m/s. So, what, could we use this formula, you might think of a way that, to how we do it, but since the acceleration is constant and you can only do is when the acceleration is constant and most of what you’ll encounter in t he first year of grades schools is acceleration Well, be constant and specially when you’re dealing with gravity the acceleration. Well, be constant. You can actually take the average velocity to figure out the distance. So, what was the average velocity over the two seconds? Well, my final velocity was 20m/s and my initial velocity was 0m/s and obviously I went kind of continuously over that, over those two seconds from zero to 20. So my average velocity, let’s call that, actually never seen it done this way before but let’s just call it average velocity is equal to the final velocity plus the initial velocity divided by two. I just took the average of the initial and the final which is 20 + 0 which is 20 divided by two which is equal to 10m/s. So, when I just― right when I let go of the rock or the ball or the penny or whatever I’m dropping, the thing is stationary, so it’s 0m/s. After two seconds we use this acceleration formula, after two seconds it accelerated it with 20 m/s and over the course of that two seconds its average velocity was 10m/s. So, we can now use that average velocity in this formula right here. So the average velocity, distance equals average velocity times time, you can kind a make mental foot note, it’s average velocity times time when the velocity is changing and acceleration is constant which is most if what you Well, see and in most projectile motion problems. So now we could say distance is equal to the average velocity times time which equal 10m/s times two seconds, once again the S is cancel out, so were 20m. So after two seconds not only is my velocity 20m/s down, once again if I said speed it would just be 20m/s but velocity is 20m/s down, nut my distance is the ball or the rock, whatever, assuming no air resistance has drop 20m. So, let’s see if we can use that― and hopefully that’s makes a little bit of intuition for you and if you are taking physics which you don’t have to view this videos that’s the idea, I want to show that this is actually exactly like one of the formula that you Well, see in your physics and it’s kind of a shame people tend to just memorizing physics without, in there―. Let me project our motion― without really appreciating that it just come from distance is equal to velocity times time and velocity is equal to― and actually let me you know, before I said velocity is equal to acceleration times time let me just expand that a little bit because I assume that my initial velocity is zero. Let me just say that the final velocity is equal to the initial velocity because you could already be going 10m/s and then you’re going to accelerate. So, the final velocity is equal to the initial velocity. This is an I plus acceleration times time. And we said that the distance― we could rewrite this―. This is the distance is equal to the average velocity times time. And then I just realized how funny that characters is― This is an I so the final velocity is equal to the initial velocity plus acceleration times time and the distance is equal to the average velocity times time. So, let’s see if we can use these two formulas which we essentially just applied in the previous example, we didn’t do it exactly to come up with the formula for distance given acceleration and time. Well, we know that the average velocity― I’ll switch colors― t eh average velocity is equal to the final velocity plus the initial velocity divided by two. Well, what is the final velocity? Well,, the final velocity is equal to this, so Well, substitute, so we have the initial velocity plus acceleration times time plus the initial velocity― my eyes are getting blurred we’re not showing―. This is where all I’s form initial velocity and it looks likes a two― but I think you can get the idea. That is all initial velocity all of that over two. So, the average velocity is equal to the initial velocity plus acceleration times time plus the initial velocity all of that divided by two, Well, that just equals two times the initial velocity, and that looks an I now, plus acceleration times time divided by two that equals the initial velocity plus acceleration times time divided by two and this might be intuitive for you as well that the average velocity is equal to your initial velocity plus ― this is essentially the difference between the how much you’re accelerating over that time and speed plus it’s going to be that divided by two because we’re taking the average. If I what I just said confuse you don’t worry about it you could just back tract at what we say it for and you think about a while this stuff, a lot of this formulas yourself and pug in numbers and I think it’ll start to make more sense. So, we figure out that the average velocity is equal to the initial velocity plus acceleration times time, so we could just substitute that back into this original equation. And once again I’m running out of time so, I’ll see you shortly.

Khan Academy

The Khan Academy is a not-for-profit organization with the mission of providing a high quality education to anyone, anywhere.

http://www.khanacademy.org/

Introduction to motion - part 2

All right, so where I left off in the last presentation I was dropping penny from the top of a building. Once again you should not do because you can kill somebody.

So, let’s say I have here, here’s the building, here’s the bad person who’s going to drop something. And let’s say they just hold it out and it just drops, the penny drops.

So, the penny is going to accelerate at the rate of gravity, so it’s going to accelerate at 10m/s2. So, let’s start with an interesting question. After 2sec, so, when T=― and let’s say they drop at right T=0. So after 2sec, after 2sec, how fast is it going? So, time is equal to 2sec or we can even say this changing we are assuming that we are starting a time equals zero, so time and changing is the same thing. If time is equal to two seconds how fast is going to be going after three seconds.

Well,, let’s use that formula, velocity is equal to acceleration, Well, acceleration is the acceleration of gravity, so, that’s 10m/s2, velocity Well, be 10m/s2 times time, times two second, times two second, two seconds. Well, we can just, velocity, we can multiply the numbers, we got 20 and then just like the numbers you can treat the units almost like variables the seconds is the same thing as S, right?

So, this S is going to be the numerator and you have S2 in the denominator. So the S, at least this S Well, cancel out with one of the two Ss’ and I multiply down here. So I Well, up with― Well, actually let me right down― it Well, be 10m/s2 and that’s the same thing as 20, that cancels out and this may set one, so that equals 20m/s.

So, you starting get a little of intuition why acceleration units are m/s2. So after two seconds we’re going 20m/s. Now let me ask you a slightly more difficult problem that not might be obvious to you.

After two seconds, how far has the penny gone? Well, this is interesting. We have this formula here, distance is equal to velocity times time. But the velocity is changing the entire time, we know after two seconds the velocity is 20m/s, so we could call this the final velocity, so let’s just call that V sub F, that’s just a fancy way of saying final velocity.

But, right when we start at T equals zero what was the velocity. Well, right when I started the initial velocity V sub for initial is equal to 0m/s. So, what, could we use this formula, you might think of a way that, to how we do it, but since the acceleration is constant and you can only do is when the acceleration is constant and most of what you’ll encounter in t he first year of grades schools is acceleration Well, be constant and specially when you’re dealing with gravity the acceleration. Well, be constant.

You can actually take the average velocity to figure out the distance. So, what was the average velocity over the two seconds? Well, my final velocity was 20m/s and my initial velocity was 0m/s and obviously I went kind of continuously over that, over those two seconds from zero to 20. So my average velocity, let’s call that, actually never seen it done this way before but let’s just call it average velocity is equal to the final velocity plus the initial velocity divided by two. I just took the average of the initial and the final which is 20 + 0 which is 20 divided by two which is equal to 10m/s.

So, when I just― right when I let go of the rock or the ball or the penny or whatever I’m dropping, the thing is stationary, so it’s 0m/s. After two seconds we use this acceleration formula, after two seconds it accelerated it with 20 m/s and over the course of that two seconds its average velocity was 10m/s.

So, we can now use that average velocity in this formula right here. So the average velocity, distance equals average velocity times time, you can kind a make mental foot note, it’s average velocity times time when the velocity is changing and acceleration is constant which is most if what you Well, see and in most projectile motion problems.

So now we could say distance is equal to the average velocity times time which equal 10m/s times two seconds, once again the S is cancel out, so were 20m. So after two seconds not only is my velocity 20m/s down, once again if I said speed it would just be 20m/s but velocity is 20m/s down, nut my distance is the ball or the rock, whatever, assuming no air resistance has drop 20m.

So, let’s see if we can use that― and hopefully that’s makes a little bit of intuition for you and if you are taking physics which you don’t have to view this videos that’s the idea, I want to show that this is actually exactly like one of the formula that you Well, see in your physics and it’s kind of a shame people tend to just memorizing physics without, in there―.

Let me project our motion― without really appreciating that it just come from distance is equal to velocity times time and velocity is equal to― and actually let me you know, before I said velocity is equal to acceleration times time let me just expand that a little bit because I assume that my initial velocity is zero. Let me just say that the final velocity is equal to the initial velocity because you could already be going 10m/s and then you’re going to accelerate. So, the final velocity is equal to the initial velocity. This is an I plus acceleration times time.

And we said that the distance― we could rewrite this―. This is the distance is equal to the average velocity times time. And then I just realized how funny that characters is― This is an I so the final velocity is equal to the initial velocity plus acceleration times time and the distance is equal to the average velocity times time.

So, let’s see if we can use these two formulas which we essentially just applied in the previous example, we didn’t do it exactly to come up with the formula for distance given acceleration and time. Well, we know that the average velocity― I’ll switch colors― t eh average velocity is equal to the final velocity plus the initial velocity divided by two.

Well, what is the final velocity? Well,, the final velocity is equal to this, so Well, substitute, so we have the initial velocity plus acceleration times time plus the initial velocity― my eyes are getting blurred we’re not showing―. This is where all I’s form initial velocity and it looks likes a two― but I think you can get the idea. That is all initial velocity all of that over two.

So, the average velocity is equal to the initial velocity plus acceleration times time plus the initial velocity all of that divided by two, Well, that just equals two times the initial velocity, and that looks an I now, plus acceleration times time divided by two that equals the initial velocity plus acceleration times time divided by two and this might be intuitive for you as well that the average velocity is equal to your initial velocity plus ― this is essentially the difference between the how much you’re accelerating over that time and speed plus it’s going to be that divided by two because we’re taking the average.

If I what I just said confuse you don’t worry about it you could just back tract at what we say it for and you think about a while this stuff, a lot of this formulas yourself and pug in numbers and I think it’ll start to make more sense.

So, we figure out that the average velocity is equal to the initial velocity plus acceleration times time, so we could just substitute that back into this original equation. And once again I’m running out of time so, I’ll see you shortly.

Transcription by: Scribe4you Transcription Services