1 00:00:03,550 --> 00:00:06,120 We will now like to begin our analysis of motion. 2 00:00:06,120 --> 00:00:07,960 And we'll start with one dimensional motion. 3 00:00:07,960 --> 00:00:12,060 Let's just consider a person running along a road. 4 00:00:12,060 --> 00:00:16,780 And so here's our runner, and here's our road. 5 00:00:16,780 --> 00:00:19,760 And what we want to do is be able to describe 6 00:00:19,760 --> 00:00:23,710 the position, the velocity, the acceleration of this runner. 7 00:00:23,710 --> 00:00:27,140 In order to do that, we need our first mathematical tool, 8 00:00:27,140 --> 00:00:29,680 which is a coordinate system. 9 00:00:29,680 --> 00:00:31,160 What is a coordinate system? 10 00:00:31,160 --> 00:00:35,650 Well, the first thing that we want to choose is an origin. 11 00:00:35,650 --> 00:00:37,530 We can pick the origin anywhere we want. 12 00:00:37,530 --> 00:00:38,940 That's a degree of freedom. 13 00:00:38,940 --> 00:00:43,970 So let's choose a point along our road as our origin. 14 00:00:43,970 --> 00:00:47,520 The next thing to do is to choose an axis. 15 00:00:47,520 --> 00:00:49,520 Well, the road is naturally defining 16 00:00:49,520 --> 00:00:51,080 an axis for our problem. 17 00:00:51,080 --> 00:00:54,650 And so we'll call this the x-axis. 18 00:00:54,650 --> 00:00:56,790 Now, along with that axis, we want 19 00:00:56,790 --> 00:01:00,170 to divide that up into some type of units 20 00:01:00,170 --> 00:01:04,730 so we might divide our axis like this. 21 00:01:04,730 --> 00:01:07,480 And what's important here is to introduce 22 00:01:07,480 --> 00:01:11,160 a positive coordinate direction. 23 00:01:11,160 --> 00:01:15,100 And so the way I'll do that, is I'll call this the plus x, 24 00:01:15,100 --> 00:01:19,550 and on this side of the origin x is negative. 25 00:01:19,550 --> 00:01:23,300 Now, the third most important thing 26 00:01:23,300 --> 00:01:26,560 is that we're going to talk about vectors and physics. 27 00:01:26,560 --> 00:01:29,934 So we want a choice of unit vector. 28 00:01:29,934 --> 00:01:31,850 Now, because it's only one dimensional motion, 29 00:01:31,850 --> 00:01:33,770 we only need one unit vector. 30 00:01:33,770 --> 00:01:39,200 So what that means is a choice of unit vector at every point. 31 00:01:39,200 --> 00:01:42,570 Let's just consider a point here, P1. 32 00:01:42,570 --> 00:01:47,050 So our unit vector I'll call it i hat 1. 33 00:01:47,050 --> 00:01:49,000 Now, let's pick another point here. 34 00:01:49,000 --> 00:01:51,070 We'll call this the point P2. 35 00:01:51,070 --> 00:01:55,039 And over here we'll choose a unit vector, i hat 2. 36 00:01:55,039 --> 00:01:59,250 So every single point in space has a unit vector. 37 00:01:59,250 --> 00:02:01,510 Now, what's unique about this one 38 00:02:01,510 --> 00:02:04,230 dimensional linear Cartesian coordinate 39 00:02:04,230 --> 00:02:07,780 system is the following, these unit vectors 40 00:02:07,780 --> 00:02:10,990 have the same magnitude-- a unit vector by definition 41 00:02:10,990 --> 00:02:17,050 has magnitude 1-- and they're pointing in the same direction. 42 00:02:17,050 --> 00:02:19,720 So if two vectors have the same magnitude 43 00:02:19,720 --> 00:02:23,010 and point in the same direction, they are equal. 44 00:02:23,010 --> 00:02:25,930 So what makes this coordinate system unique, 45 00:02:25,930 --> 00:02:27,470 this Cartesian coordinate system, 46 00:02:27,470 --> 00:02:31,180 that every single point, no matter where we are, 47 00:02:31,180 --> 00:02:34,680 the unit vectors point in the positive direction 48 00:02:34,680 --> 00:02:36,910 because they have the same magnitude and direction. 49 00:02:36,910 --> 00:02:39,700 All of these unit vectors are equal. 50 00:02:39,700 --> 00:02:42,000 And we call that i hat. 51 00:02:42,000 --> 00:02:45,800 So symbolically, we may draw a picture 52 00:02:45,800 --> 00:02:50,180 and indicate our unit vector in the positive x direction. 53 00:02:50,180 --> 00:02:52,680 And this is our coordinate system. 54 00:02:52,680 --> 00:02:54,720 And we can next begin to describe 55 00:02:54,720 --> 00:02:58,070 the position and the velocity of our object 56 00:02:58,070 --> 00:03:01,324 as it's moving along this x direction.