WEBVTT 00:00:03.550 --> 00:00:06.120 We will now like to begin our analysis of motion. 00:00:06.120 --> 00:00:07.960 And we'll start with one dimensional motion. 00:00:07.960 --> 00:00:12.060 Let's just consider a person running along a road. 00:00:12.060 --> 00:00:16.780 And so here's our runner, and here's our road. 00:00:16.780 --> 00:00:19.760 And what we want to do is be able to describe 00:00:19.760 --> 00:00:23.710 the position, the velocity, the acceleration of this runner. 00:00:23.710 --> 00:00:27.140 In order to do that, we need our first mathematical tool, 00:00:27.140 --> 00:00:29.680 which is a coordinate system. 00:00:29.680 --> 00:00:31.160 What is a coordinate system? 00:00:31.160 --> 00:00:35.650 Well, the first thing that we want to choose is an origin. 00:00:35.650 --> 00:00:37.530 We can pick the origin anywhere we want. 00:00:37.530 --> 00:00:38.940 That's a degree of freedom. 00:00:38.940 --> 00:00:43.970 So let's choose a point along our road as our origin. 00:00:43.970 --> 00:00:47.520 The next thing to do is to choose an axis. 00:00:47.520 --> 00:00:49.520 Well, the road is naturally defining 00:00:49.520 --> 00:00:51.080 an axis for our problem. 00:00:51.080 --> 00:00:54.650 And so we'll call this the x-axis. 00:00:54.650 --> 00:00:56.790 Now, along with that axis, we want 00:00:56.790 --> 00:01:00.170 to divide that up into some type of units 00:01:00.170 --> 00:01:04.730 so we might divide our axis like this. 00:01:04.730 --> 00:01:07.480 And what's important here is to introduce 00:01:07.480 --> 00:01:11.160 a positive coordinate direction. 00:01:11.160 --> 00:01:15.100 And so the way I'll do that, is I'll call this the plus x, 00:01:15.100 --> 00:01:19.550 and on this side of the origin x is negative. 00:01:19.550 --> 00:01:23.300 Now, the third most important thing 00:01:23.300 --> 00:01:26.560 is that we're going to talk about vectors and physics. 00:01:26.560 --> 00:01:29.934 So we want a choice of unit vector. 00:01:29.934 --> 00:01:31.850 Now, because it's only one dimensional motion, 00:01:31.850 --> 00:01:33.770 we only need one unit vector. 00:01:33.770 --> 00:01:39.200 So what that means is a choice of unit vector at every point. 00:01:39.200 --> 00:01:42.570 Let's just consider a point here, P1. 00:01:42.570 --> 00:01:47.050 So our unit vector I'll call it i hat 1. 00:01:47.050 --> 00:01:49.000 Now, let's pick another point here. 00:01:49.000 --> 00:01:51.070 We'll call this the point P2. 00:01:51.070 --> 00:01:55.039 And over here we'll choose a unit vector, i hat 2. 00:01:55.039 --> 00:01:59.250 So every single point in space has a unit vector. 00:01:59.250 --> 00:02:01.510 Now, what's unique about this one 00:02:01.510 --> 00:02:04.230 dimensional linear Cartesian coordinate 00:02:04.230 --> 00:02:07.780 system is the following, these unit vectors 00:02:07.780 --> 00:02:10.990 have the same magnitude-- a unit vector by definition 00:02:10.990 --> 00:02:17.050 has magnitude 1-- and they're pointing in the same direction. 00:02:17.050 --> 00:02:19.720 So if two vectors have the same magnitude 00:02:19.720 --> 00:02:23.010 and point in the same direction, they are equal. 00:02:23.010 --> 00:02:25.930 So what makes this coordinate system unique, 00:02:25.930 --> 00:02:27.470 this Cartesian coordinate system, 00:02:27.470 --> 00:02:31.180 that every single point, no matter where we are, 00:02:31.180 --> 00:02:34.680 the unit vectors point in the positive direction 00:02:34.680 --> 00:02:36.910 because they have the same magnitude and direction. 00:02:36.910 --> 00:02:39.700 All of these unit vectors are equal. 00:02:39.700 --> 00:02:42.000 And we call that i hat. 00:02:42.000 --> 00:02:45.800 So symbolically, we may draw a picture 00:02:45.800 --> 00:02:50.180 and indicate our unit vector in the positive x direction. 00:02:50.180 --> 00:02:52.680 And this is our coordinate system. 00:02:52.680 --> 00:02:54.720 And we can next begin to describe 00:02:54.720 --> 00:02:58.070 the position and the velocity of our object 00:02:58.070 --> 00:03:01.324 as it's moving along this x direction.