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Introduction to the kinematic equations - Contenido educativo

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Subido el 21 de abril de 2022 por Juan C. F.

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Welcome to the Physics Classroom's video tutorial on kinematics. 00:00:00
The topic of this video is Introduction to Kinematic Equations. 00:00:04
And there's just two questions we wish to answer in this video. 00:00:09
They are, what are the four kinematic equations and what do the symbols 00:00:12
in these equations mean? And how do you use these four equations 00:00:16
to solve physics word problems? Let's get started. 00:00:20
Classical mechanics, of which kinematics is a branch of, 00:00:25
has the ability to make very precise and detailed predictions about the future 00:00:28
state of motion of an object. For instance, if we know some information 00:00:32
about the current state of motion, say the original position and say the 00:00:36
speed and the acceleration, we could predict at some later 00:00:40
moment in time the actual position of that object. 00:00:44
And this is what the kinematic equations are all about. 00:00:48
Let's look at the four kinematic equations here. You'll notice that 00:00:52
in the diagram, four equations are listed and on the left side of the equation is a variable 00:00:56
and on the right side of the equation are a collection of terms containing variables. Now 00:01:01
one of the most important things that you need to get used to right away is what are the meanings 00:01:07
of these variables? What do the symbols mean? So D stands for the displacement of the object, 00:01:11
the overall change in position. The acceleration is represented by the symbol A and the time is 00:01:18
represented by the symbol t in these equations. Now you'll notice there's a few v's in these 00:01:25
equations. There's a v with a little o after it and a v with a little f after it. These stand for 00:01:31
velocities like v with an o after it stands for the original velocity and a v with an f after it 00:01:37
stands for the final velocity. These are the four kinematic equations and they all assume one thing 00:01:44
that over the course of motion, the acceleration value that you see in these equations is constant. 00:01:51
One thing that you should be aware of is that the appearance of these four kinematic equations 00:01:57
may vary from course to course and teacher to teacher. 00:02:02
For instance, one of the first things that you might notice is that the D that you see in my equation 00:02:06
stands for displacement, and other courses and other teachers and other sources may represent it by a delta X, 00:02:10
where delta x refers to the change in position just like d represents the change in position 00:02:17
so if you put a delta x into the d spot in the first equation you would have on the left side 00:02:23
x final minus x original and maybe you could move that x original over to the right side and you'd 00:02:31
have an equation that looks like this where the x stands for position x or x original stands for 00:02:38
the final position and the original position. In the other equations, we often see a delta x 00:02:45
inserted in for d in the equation. A second variation that you might find is instead of 00:02:51
seeing t, you might see some delta t's in there. It still means the same thing, the time over which 00:02:58
the motion took place. And then you might notice that the v original that I have, the v subscripted 00:03:05
O may be replaced with a V subscripted I. They mean the same thing. The I just means initial 00:03:12
velocity as opposed to original velocity, just a different way of putting it. So these four 00:03:19
equations may not always look like the way that I've placed them here, but the main thing that 00:03:25
you need to understand is whatever form of the equation you use, what do the symbols mean? So 00:03:30
here they are again for my four equations. Another thing that you should be aware of as you use these 00:03:37
kinematic equations or see others such as your friends, your enemies, or your teachers using 00:03:44
these equations is that on occasion there are special conditions that alter the form of these 00:03:49
equations. For instance, somebody might be solving a problem in which originally the object starts 00:03:54
from rest. In such a case, the V-O terms that you see in these equations end up dropping out of the 00:03:59
equations, so they might be rewritten as shown here. So always be on the lookout for a phrase 00:04:06
in the problem that you're trying to solve that says starting from rest or beginning in a resting 00:04:12
position, because in those situations, under those conditions, the kinematic equations may simplify 00:04:19
to the form that you see here. A second set of conditions that you might come across is an object 00:04:25
could come to rest or come to a stopping position. In situations such as this, the final velocity 00:04:31
would be zero, and anywhere you see the final velocity in these equations, those terms would 00:04:39
drop out. So the equations would change into these forms. Now if you look at the second equation in 00:04:44
particular, that looks quite different than the second equation on the left. What I've done is 00:04:51
I've dropped out the vf squared term and then I swung the 2ad over to the opposite side such that 00:04:56
there's a negative in front of it. You just need to be aware that depending upon the conditions of 00:05:03
the problems for which you're using the equations, that the form could be different than what is 00:05:09
shown in my original four kinematic equations. A person could make an effort to use these big 00:05:14
four kinematic equations in a problem which the object moves with a constant velocity. 00:05:21
In such instances, the acceleration is zero, and any term that has a in it will drop out of the equation. 00:05:25
But there's another variation that occurs in this situation, and that is if the velocity is constant, 00:05:33
then it doesn't even make sense to distinguish between the original velocity and the final velocity, 00:05:39
since there really isn't two velocities, there's just one constant velocity. 00:05:45
So when we have a constant velocity problem, the equations turn to this form. 00:05:50
You'll notice the first and the third equation have some meaning. 00:05:56
Distance equal velocity times time. 00:05:59
That's just simply the rate equation that you've probably known for some time. 00:06:02
You'll also notice that the second and the fourth equation are not useful at all. 00:06:06
Certainly you don't need to know physics in order to tell that the final velocity is equal to the original velocity when it's not changing. 00:06:10
These big four equations are typically not used for constant velocity problems. 00:06:17
We just typically use d equal to v times t. 00:06:22
But we instead use these four equations for accelerating problems in which there's an acceleration. 00:06:24
And now we get to the useful part, learning how to use the kinematic equations to solve physics word problems. 00:06:31
So what we've seen so far is that there are five variables in these equations, 00:06:38
but not a single one of the equations contains five variable values in it. 00:06:43
In fact, each equation has four variables in it, four symbols. 00:06:49
So the strategy that we use to solve a problem is to look through a problem like the one that you see here 00:06:54
and try to find three known values in order to solve for the fourth variable that the problem requests. 00:07:01
For instance, here we see 18.5 meters per second, 46.1 meters per second, and 2.47 seconds. 00:07:10
This is the V original, the V final, and the time. 00:07:20
And what we're looking for is a distance value. 00:07:23
And so we are going to look for the one equation that has VL, VF, T, and D in it, 00:07:26
and that's the equation that we'll use to solve this problem. 00:07:34
So the basic strategy will go something like this. 00:07:38
First, we're going to read the problem carefully, 00:07:42
and we're going to identify all known values of at least three of the five variables. 00:07:45
In fact, we're going to write down the known values 00:07:50
and relate these values to the symbols that are used in the equations. 00:07:52
For instance, we might say something like v original equal 15 meters per second. 00:07:56
Then we're going to identify the unknown variable. 00:08:02
We're going to write it in symbol form. 00:08:06
For instance, we might say, find the D. 00:08:07
Now that you have four variable symbols, three with known values and one with an unknown value, 00:08:11
you're going to look through the list of four equations and find the one equation that contains these four variables. 00:08:16
Once you've found it, write it down. 00:08:23
Then you're going to substitute the known values into this equation, 00:08:26
and you're going to use some algebra and calculations to solve for the unknown variable value. 00:08:30
Sounds easy, doesn't it? 00:08:36
Well, let's give it a try. 00:08:37
So here's our example problem. 00:08:39
And what we're going to do is we're going to use the strategy that's listed here on the right side of the slide in order to solve this problem. 00:08:42
And the first step of the strategy is to look through the problem and identify three variables whose values are known. 00:08:48
So a car starts from rest. 00:08:56
And I see that starts from rest. 00:08:58
And that's an indicator to me that the original velocity is zero. 00:09:00
And it accelerates over a time of 5.21 seconds, so I know the time. 00:09:04
And for a distance of 112 meters, so I know a distance. 00:09:09
And so what I'm asked to do is to write these things down and equate the values to the actual symbols used in the equation. 00:09:14
And you see how I've done this right there. 00:09:22
That's step one. 00:09:25
Now I look for what am I trying to find. 00:09:26
Identify the unknown and write it down in symbol form. 00:09:29
and I'm looking for the acceleration, determine the acceleration of the car. 00:09:32
So what I do is I write down A equal question mark or find A or something like that. 00:09:37
Now I have four variables, and what I'm going to do is find the equation that has these four variables in it. 00:09:41
So here's the list of four, and I'm looking for the one equation that has the original D, T, and A. 00:09:49
So just start at the top of the list and go down from top to bottom, looking to see which equation has these four variables in it. 00:09:57
And wouldn't you know, it's the top equation. 00:10:06
So now I'm going to write that top equation down. 00:10:08
Now I get to step four, where I substitute known values into the equation. 00:10:11
And one thing that I notice is that the original velocity is zero. 00:10:16
So that means that that term that goes VO times T is actually going to cancel out. 00:10:20
And the equation is going to simplify to D equal 1 half A times T squared. 00:10:27
So I take my value for D and I take my value for T and I substitute it into the equation. 00:10:33
Now I'm going to do some algebra and calculations to solve for this unknown value, A, the acceleration. 00:10:41
I'm just going to make sure I follow all the rules of algebra. 00:10:49
And when I do, I end up getting the acceleration to be 8.25 meters per second squared. 00:10:53
And that's how you use this five-step strategy to solve a kinematic equation problem. 00:11:00
Now there's one final caution that I'd like to give you. 00:11:07
In these equations, we see displacement, velocity, and acceleration. 00:11:10
And all three of these quantities are vector quantities. 00:11:14
And just like any vector quantity, they're more than just a number. 00:11:18
They have a magnitude or numerical value, but they also have a direction. 00:11:22
And oftentimes directions are represented by plus and minus symbols when we're using math. 00:11:26
So it's very important that you include the directional information 00:11:32
in the equations when you're solving for an unknown. 00:11:36
For instance, here you see that a car is approaching an intersection at 24 meters per second 00:11:40
and it brakes to a stop. 00:11:45
So I know an original velocity, and I know a final velocity, and I'm told the car is losing 00:11:47
eight meters per second every second. Determine the braking distance. So when I write down my 00:11:53
known variable values, I'm going to have to be very careful because this acceleration value 00:12:00
is a negative eight meters per second per second. And so when I do this problem, it's important that 00:12:05
I substitute in negative 8 in the place of a when solving for my unknown 00:12:12
distance well we've done it we've accomplished the purpose we now know 00:12:18
what the four kinematic equations are and what the symbols represent and we 00:12:24
have a fairly decent idea as to how to use the equations in order to solve 00:12:28
physics word problems it's at this point in every video that I like to give you 00:12:32
some help a way to make the learning stick I'd like to give you a learning 00:12:36
action plan to help you make this learning stick and stay with you for a 00:12:40
while but before I do I was wondering if I could ask you to help us out if you 00:12:45
liked the video why don't you press the like button down below and give us a 00:12:49
like and if you liked the video maybe you'd like to have more videos like this 00:12:53
why don't you subscribe to our channel and if you do you'll get notifications 00:12:56
whenever a new video comes out there's gonna be a whole lot of those coming out 00:13:00
this year and finally if you have a question or a comment why don't you 00:13:03
leave it down below in the comments section now here's the learning action 00:13:07
plan first thing I'd like to suggest that maybe you do is head off to our 00:13:11
website you'll see a section there called the calculator pad and when you 00:13:14
go to the calculator plan what you're going to get is a whole set of problems 00:13:18
along with answers along with audio guided help now if you're trying to 00:13:21
practice kinematic equations go to the 1d kinematics section look for questions 00:13:27
18 through 35. Every one of those questions has to do with, in one way or another, with the use of 00:13:32
kinematic equations. Another place on our website where you can find some help is in the review 00:13:38
session section. Now this is generally used to review for tests and quizzes and such, but you 00:13:43
can go there at any point when you're trying to learn kinematic equations. You can go to the 00:13:49
kinematics section of the review session and do questions 43 through 50. And finally, we have a 00:13:53
page on our website in which there are 20 kinematic equation problems answers and very 00:14:00
thorough worked out solutions to those problems. It's in the physics classroom tutorial and I have 00:14:05
a link to that page down below. In fact, all of these resources are linked to in the description 00:14:11
section below this video. Well, whatever you do, I wish you the best of luck. Good luck to you. 00:14:16
Idioma/s:
en
Autor/es:
The Physics classroom
Subido por:
Juan C. F.
Licencia:
Reconocimiento - No comercial - Compartir igual
Visualizaciones:
69
Fecha:
21 de abril de 2022 - 10:44
Visibilidad:
Público
Enlace Relacionado:
https://www.youtube.com/watch?v=snH0sy-qyv0
Centro:
IES CLARA CAMPOAMOR
Duración:
14′ 22″
Relación de aspecto:
1.78:1
Resolución:
1280x718 píxeles
Tamaño:
39.28 MBytes

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