1 00:00:00,490 --> 00:00:04,490 Welcome to the Physics Classroom's video tutorial on kinematics. 2 00:00:04,950 --> 00:00:08,429 The topic of this video is Introduction to Kinematic Equations. 3 00:00:09,669 --> 00:00:12,390 And there's just two questions we wish to answer in this video. 4 00:00:12,529 --> 00:00:16,269 They are, what are the four kinematic equations and what do the symbols 5 00:00:16,269 --> 00:00:20,489 in these equations mean? And how do you use these four equations 6 00:00:20,489 --> 00:00:24,010 to solve physics word problems? Let's get started. 7 00:00:25,050 --> 00:00:28,429 Classical mechanics, of which kinematics is a branch of, 8 00:00:28,429 --> 00:00:32,810 has the ability to make very precise and detailed predictions about the future 9 00:00:32,810 --> 00:00:36,609 state of motion of an object. For instance, if we know some information 10 00:00:36,609 --> 00:00:40,729 about the current state of motion, say the original position and say the 11 00:00:40,729 --> 00:00:44,570 speed and the acceleration, we could predict at some later 12 00:00:44,570 --> 00:00:48,149 moment in time the actual position of that object. 13 00:00:48,829 --> 00:00:51,810 And this is what the kinematic equations are all about. 14 00:00:52,450 --> 00:00:56,689 Let's look at the four kinematic equations here. You'll notice that 15 00:00:56,689 --> 00:01:01,950 in the diagram, four equations are listed and on the left side of the equation is a variable 16 00:01:01,950 --> 00:01:07,250 and on the right side of the equation are a collection of terms containing variables. Now 17 00:01:07,250 --> 00:01:11,709 one of the most important things that you need to get used to right away is what are the meanings 18 00:01:11,709 --> 00:01:18,250 of these variables? What do the symbols mean? So D stands for the displacement of the object, 19 00:01:18,370 --> 00:01:25,950 the overall change in position. The acceleration is represented by the symbol A and the time is 20 00:01:25,950 --> 00:01:31,390 represented by the symbol t in these equations. Now you'll notice there's a few v's in these 21 00:01:31,390 --> 00:01:37,609 equations. There's a v with a little o after it and a v with a little f after it. These stand for 22 00:01:37,609 --> 00:01:44,390 velocities like v with an o after it stands for the original velocity and a v with an f after it 23 00:01:44,390 --> 00:01:51,150 stands for the final velocity. These are the four kinematic equations and they all assume one thing 24 00:01:51,150 --> 00:01:57,230 that over the course of motion, the acceleration value that you see in these equations is constant. 25 00:01:57,730 --> 00:02:02,189 One thing that you should be aware of is that the appearance of these four kinematic equations 26 00:02:02,189 --> 00:02:05,469 may vary from course to course and teacher to teacher. 27 00:02:06,010 --> 00:02:10,849 For instance, one of the first things that you might notice is that the D that you see in my equation 28 00:02:10,849 --> 00:02:17,210 stands for displacement, and other courses and other teachers and other sources may represent it by a delta X, 29 00:02:17,210 --> 00:02:23,689 where delta x refers to the change in position just like d represents the change in position 30 00:02:23,689 --> 00:02:31,110 so if you put a delta x into the d spot in the first equation you would have on the left side 31 00:02:31,110 --> 00:02:38,169 x final minus x original and maybe you could move that x original over to the right side and you'd 32 00:02:38,169 --> 00:02:45,189 have an equation that looks like this where the x stands for position x or x original stands for 33 00:02:45,189 --> 00:02:51,610 the final position and the original position. In the other equations, we often see a delta x 34 00:02:51,610 --> 00:02:58,930 inserted in for d in the equation. A second variation that you might find is instead of 35 00:02:58,930 --> 00:03:05,569 seeing t, you might see some delta t's in there. It still means the same thing, the time over which 36 00:03:05,569 --> 00:03:12,530 the motion took place. And then you might notice that the v original that I have, the v subscripted 37 00:03:12,530 --> 00:03:19,210 O may be replaced with a V subscripted I. They mean the same thing. The I just means initial 38 00:03:19,210 --> 00:03:25,030 velocity as opposed to original velocity, just a different way of putting it. So these four 39 00:03:25,030 --> 00:03:30,650 equations may not always look like the way that I've placed them here, but the main thing that 40 00:03:30,650 --> 00:03:37,349 you need to understand is whatever form of the equation you use, what do the symbols mean? So 41 00:03:37,349 --> 00:03:44,810 here they are again for my four equations. Another thing that you should be aware of as you use these 42 00:03:44,810 --> 00:03:49,370 kinematic equations or see others such as your friends, your enemies, or your teachers using 43 00:03:49,370 --> 00:03:54,509 these equations is that on occasion there are special conditions that alter the form of these 44 00:03:54,509 --> 00:03:59,889 equations. For instance, somebody might be solving a problem in which originally the object starts 45 00:03:59,889 --> 00:04:06,509 from rest. In such a case, the V-O terms that you see in these equations end up dropping out of the 46 00:04:06,509 --> 00:04:12,629 equations, so they might be rewritten as shown here. So always be on the lookout for a phrase 47 00:04:12,629 --> 00:04:19,149 in the problem that you're trying to solve that says starting from rest or beginning in a resting 48 00:04:19,149 --> 00:04:25,629 position, because in those situations, under those conditions, the kinematic equations may simplify 49 00:04:25,629 --> 00:04:31,949 to the form that you see here. A second set of conditions that you might come across is an object 50 00:04:31,949 --> 00:04:39,329 could come to rest or come to a stopping position. In situations such as this, the final velocity 51 00:04:39,329 --> 00:04:44,910 would be zero, and anywhere you see the final velocity in these equations, those terms would 52 00:04:44,910 --> 00:04:51,410 drop out. So the equations would change into these forms. Now if you look at the second equation in 53 00:04:51,410 --> 00:04:56,810 particular, that looks quite different than the second equation on the left. What I've done is 54 00:04:56,810 --> 00:05:03,649 I've dropped out the vf squared term and then I swung the 2ad over to the opposite side such that 55 00:05:03,649 --> 00:05:09,110 there's a negative in front of it. You just need to be aware that depending upon the conditions of 56 00:05:09,110 --> 00:05:14,529 the problems for which you're using the equations, that the form could be different than what is 57 00:05:14,529 --> 00:05:21,230 shown in my original four kinematic equations. A person could make an effort to use these big 58 00:05:21,230 --> 00:05:25,769 four kinematic equations in a problem which the object moves with a constant velocity. 59 00:05:25,769 --> 00:05:32,850 In such instances, the acceleration is zero, and any term that has a in it will drop out of the equation. 60 00:05:33,329 --> 00:05:39,329 But there's another variation that occurs in this situation, and that is if the velocity is constant, 61 00:05:39,750 --> 00:05:45,170 then it doesn't even make sense to distinguish between the original velocity and the final velocity, 62 00:05:45,370 --> 00:05:50,370 since there really isn't two velocities, there's just one constant velocity. 63 00:05:50,910 --> 00:05:55,850 So when we have a constant velocity problem, the equations turn to this form. 64 00:05:56,230 --> 00:05:59,050 You'll notice the first and the third equation have some meaning. 65 00:05:59,550 --> 00:06:01,790 Distance equal velocity times time. 66 00:06:02,149 --> 00:06:05,769 That's just simply the rate equation that you've probably known for some time. 67 00:06:06,170 --> 00:06:09,750 You'll also notice that the second and the fourth equation are not useful at all. 68 00:06:10,170 --> 00:06:16,949 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. 69 00:06:17,629 --> 00:06:22,089 These big four equations are typically not used for constant velocity problems. 70 00:06:22,209 --> 00:06:24,350 We just typically use d equal to v times t. 71 00:06:24,610 --> 00:06:30,610 But we instead use these four equations for accelerating problems in which there's an acceleration. 72 00:06:31,850 --> 00:06:38,410 And now we get to the useful part, learning how to use the kinematic equations to solve physics word problems. 73 00:06:38,910 --> 00:06:43,709 So what we've seen so far is that there are five variables in these equations, 74 00:06:43,709 --> 00:06:49,250 but not a single one of the equations contains five variable values in it. 75 00:06:49,250 --> 00:06:54,449 In fact, each equation has four variables in it, four symbols. 76 00:06:54,990 --> 00:07:01,389 So the strategy that we use to solve a problem is to look through a problem like the one that you see here 77 00:07:01,389 --> 00:07:10,389 and try to find three known values in order to solve for the fourth variable that the problem requests. 78 00:07:10,389 --> 00:07:19,750 For instance, here we see 18.5 meters per second, 46.1 meters per second, and 2.47 seconds. 79 00:07:20,269 --> 00:07:23,410 This is the V original, the V final, and the time. 80 00:07:23,810 --> 00:07:26,329 And what we're looking for is a distance value. 81 00:07:26,930 --> 00:07:34,470 And so we are going to look for the one equation that has VL, VF, T, and D in it, 82 00:07:34,810 --> 00:07:38,110 and that's the equation that we'll use to solve this problem. 83 00:07:38,769 --> 00:07:42,110 So the basic strategy will go something like this. 84 00:07:42,509 --> 00:07:44,889 First, we're going to read the problem carefully, 85 00:07:45,370 --> 00:07:50,490 and we're going to identify all known values of at least three of the five variables. 86 00:07:50,930 --> 00:07:52,990 In fact, we're going to write down the known values 87 00:07:52,990 --> 00:07:56,850 and relate these values to the symbols that are used in the equations. 88 00:07:56,850 --> 00:08:02,550 For instance, we might say something like v original equal 15 meters per second. 89 00:08:02,910 --> 00:08:05,930 Then we're going to identify the unknown variable. 90 00:08:06,170 --> 00:08:07,750 We're going to write it in symbol form. 91 00:08:07,750 --> 00:08:10,329 For instance, we might say, find the D. 92 00:08:11,089 --> 00:08:16,230 Now that you have four variable symbols, three with known values and one with an unknown value, 93 00:08:16,290 --> 00:08:23,329 you're going to look through the list of four equations and find the one equation that contains these four variables. 94 00:08:23,790 --> 00:08:25,810 Once you've found it, write it down. 95 00:08:26,350 --> 00:08:29,509 Then you're going to substitute the known values into this equation, 96 00:08:30,069 --> 00:08:35,870 and you're going to use some algebra and calculations to solve for the unknown variable value. 97 00:08:36,110 --> 00:08:37,610 Sounds easy, doesn't it? 98 00:08:37,750 --> 00:08:38,970 Well, let's give it a try. 99 00:08:39,529 --> 00:08:41,509 So here's our example problem. 100 00:08:42,110 --> 00:08:48,850 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. 101 00:08:48,850 --> 00:08:56,250 And the first step of the strategy is to look through the problem and identify three variables whose values are known. 102 00:08:56,830 --> 00:08:58,850 So a car starts from rest. 103 00:08:58,929 --> 00:09:00,289 And I see that starts from rest. 104 00:09:00,389 --> 00:09:04,389 And that's an indicator to me that the original velocity is zero. 105 00:09:04,389 --> 00:09:09,450 And it accelerates over a time of 5.21 seconds, so I know the time. 106 00:09:09,769 --> 00:09:13,970 And for a distance of 112 meters, so I know a distance. 107 00:09:14,470 --> 00:09:22,529 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. 108 00:09:22,909 --> 00:09:24,850 And you see how I've done this right there. 109 00:09:25,289 --> 00:09:26,289 That's step one. 110 00:09:26,669 --> 00:09:29,590 Now I look for what am I trying to find. 111 00:09:29,830 --> 00:09:32,730 Identify the unknown and write it down in symbol form. 112 00:09:32,730 --> 00:09:36,750 and I'm looking for the acceleration, determine the acceleration of the car. 113 00:09:37,129 --> 00:09:41,610 So what I do is I write down A equal question mark or find A or something like that. 114 00:09:41,929 --> 00:09:49,590 Now I have four variables, and what I'm going to do is find the equation that has these four variables in it. 115 00:09:49,950 --> 00:09:57,570 So here's the list of four, and I'm looking for the one equation that has the original D, T, and A. 116 00:09:57,570 --> 00:10:06,049 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. 117 00:10:06,330 --> 00:10:08,330 And wouldn't you know, it's the top equation. 118 00:10:08,669 --> 00:10:11,389 So now I'm going to write that top equation down. 119 00:10:11,870 --> 00:10:16,490 Now I get to step four, where I substitute known values into the equation. 120 00:10:16,610 --> 00:10:20,970 And one thing that I notice is that the original velocity is zero. 121 00:10:20,970 --> 00:10:27,649 So that means that that term that goes VO times T is actually going to cancel out. 122 00:10:27,750 --> 00:10:33,210 And the equation is going to simplify to D equal 1 half A times T squared. 123 00:10:33,509 --> 00:10:40,610 So I take my value for D and I take my value for T and I substitute it into the equation. 124 00:10:41,190 --> 00:10:48,990 Now I'm going to do some algebra and calculations to solve for this unknown value, A, the acceleration. 125 00:10:49,750 --> 00:10:53,070 I'm just going to make sure I follow all the rules of algebra. 126 00:10:53,590 --> 00:11:00,070 And when I do, I end up getting the acceleration to be 8.25 meters per second squared. 127 00:11:00,570 --> 00:11:06,309 And that's how you use this five-step strategy to solve a kinematic equation problem. 128 00:11:07,309 --> 00:11:10,110 Now there's one final caution that I'd like to give you. 129 00:11:10,110 --> 00:11:14,570 In these equations, we see displacement, velocity, and acceleration. 130 00:11:14,950 --> 00:11:17,730 And all three of these quantities are vector quantities. 131 00:11:18,370 --> 00:11:21,669 And just like any vector quantity, they're more than just a number. 132 00:11:22,250 --> 00:11:25,649 They have a magnitude or numerical value, but they also have a direction. 133 00:11:26,250 --> 00:11:32,370 And oftentimes directions are represented by plus and minus symbols when we're using math. 134 00:11:32,929 --> 00:11:36,629 So it's very important that you include the directional information 135 00:11:36,629 --> 00:11:39,850 in the equations when you're solving for an unknown. 136 00:11:40,049 --> 00:11:45,210 For instance, here you see that a car is approaching an intersection at 24 meters per second 137 00:11:45,210 --> 00:11:47,070 and it brakes to a stop. 138 00:11:47,070 --> 00:11:53,190 So I know an original velocity, and I know a final velocity, and I'm told the car is losing 139 00:11:53,190 --> 00:12:00,309 eight meters per second every second. Determine the braking distance. So when I write down my 140 00:12:00,309 --> 00:12:05,929 known variable values, I'm going to have to be very careful because this acceleration value 141 00:12:05,929 --> 00:12:12,730 is a negative eight meters per second per second. And so when I do this problem, it's important that 142 00:12:12,730 --> 00:12:18,370 I substitute in negative 8 in the place of a when solving for my unknown 143 00:12:18,370 --> 00:12:24,559 distance well we've done it we've accomplished the purpose we now know 144 00:12:24,559 --> 00:12:28,279 what the four kinematic equations are and what the symbols represent and we 145 00:12:28,279 --> 00:12:32,779 have a fairly decent idea as to how to use the equations in order to solve 146 00:12:32,779 --> 00:12:36,899 physics word problems it's at this point in every video that I like to give you 147 00:12:36,899 --> 00:12:40,879 some help a way to make the learning stick I'd like to give you a learning 148 00:12:40,879 --> 00:12:45,259 action plan to help you make this learning stick and stay with you for a 149 00:12:45,259 --> 00:12:49,940 while but before I do I was wondering if I could ask you to help us out if you 150 00:12:49,940 --> 00:12:53,259 liked the video why don't you press the like button down below and give us a 151 00:12:53,259 --> 00:12:56,480 like and if you liked the video maybe you'd like to have more videos like this 152 00:12:56,480 --> 00:13:00,679 why don't you subscribe to our channel and if you do you'll get notifications 153 00:13:00,679 --> 00:13:03,980 whenever a new video comes out there's gonna be a whole lot of those coming out 154 00:13:03,980 --> 00:13:07,220 this year and finally if you have a question or a comment why don't you 155 00:13:07,220 --> 00:13:11,000 leave it down below in the comments section now here's the learning action 156 00:13:11,000 --> 00:13:14,299 plan first thing I'd like to suggest that maybe you do is head off to our 157 00:13:14,299 --> 00:13:18,139 website you'll see a section there called the calculator pad and when you 158 00:13:18,139 --> 00:13:21,799 go to the calculator plan what you're going to get is a whole set of problems 159 00:13:21,799 --> 00:13:27,980 along with answers along with audio guided help now if you're trying to 160 00:13:27,980 --> 00:13:32,279 practice kinematic equations go to the 1d kinematics section look for questions 161 00:13:32,279 --> 00:13:38,399 18 through 35. Every one of those questions has to do with, in one way or another, with the use of 162 00:13:38,399 --> 00:13:43,299 kinematic equations. Another place on our website where you can find some help is in the review 163 00:13:43,299 --> 00:13:49,240 session section. Now this is generally used to review for tests and quizzes and such, but you 164 00:13:49,240 --> 00:13:53,559 can go there at any point when you're trying to learn kinematic equations. You can go to the 165 00:13:53,559 --> 00:14:00,379 kinematics section of the review session and do questions 43 through 50. And finally, we have a 166 00:14:00,379 --> 00:14:05,940 page on our website in which there are 20 kinematic equation problems answers and very 167 00:14:05,940 --> 00:14:11,159 thorough worked out solutions to those problems. It's in the physics classroom tutorial and I have 168 00:14:11,159 --> 00:14:16,299 a link to that page down below. In fact, all of these resources are linked to in the description 169 00:14:16,299 --> 00:14:21,879 section below this video. Well, whatever you do, I wish you the best of luck. Good luck to you.