 So now let's look at graphing position versus time. We're going to start by limiting ourselves to position in one dimension, which means position along a line. But we have a couple of choices here. We could have a horizontal line, which uses x as the variable, or a vertical line, which uses y as a variable to represent the position. Regardless of which one of these two I use, you notice that the position depends on time. So in this case what that means is that our time is the independent variable and position is the dependent variable. Now I'm stressing this right now because it changes how we make the graph. So our position versus time graph, time, the independent variable always goes along the horizontal axis. The vertical axis is for the dependent variable, which is your position. Even if it's a horizontal position, we're going to chart that position along the vertical axis. So this could be x or y, but the vertical axis is always for your position. Now here's an example where we've got some data points. So data points means that at some very specific times, in this case the individual seconds, we know what the position is. So for example, at a time of two seconds, I have a position of four meters. And at a time of eight seconds, I've got a position of minus three meters. Remember that positions can be positive or negative depending on how we've defined our zero reference point. So now we can look at time spans. For example, we could talk in a problem about what happens between the time of two seconds and six seconds. So two seconds becomes the initial time we care about, and six seconds becomes the final time that I care about. When we define time spans, we recognize that time always moves forward. And so our time span is always going to be an arrow to the right showing us how we progressed from some earlier time to some later time. If we look at displacement on the graph, we recognize that again we have to specify certain end points for our time. What time span are we talking about? Because displacement is the change in position between two different times. So if we use our same two seconds and six seconds, we first have to figure out, well, what's my position at two seconds? That's four meters. What's my position at six seconds? It's going to be one meter. So my displacement is moving from four meters to three meters, which would be a displacement of minus three meters. Now both of those examples used a graph where we had data points. But sometimes we're actually given a function for the position, an actual equation. If we're given an actual equation for the position as a function of time, then we can create a continuous graph of that particular function. And that means we don't just know the position at specific times, but we can calculate it at any particular time if you've got the formula. If you just have the graph, we can estimate the position at any specific time. So for example, here's a time of about three seconds, and we see that at that time it has a position of about two and a half meters. Not only can I get individual things, but I can talk about time ranges again. So for example, from the time span from zero to three seconds, I have a displacement that moves from one to two and a half, or a displacement of positive one and a half meters. Or I can look at some later time on the graph from six seconds up to about eleven and a half seconds and see that I've got a negative displacement over that particular time span. So you can see now that graphing your position versus time provides a real quick visual picture of what's happening, but you can also pull a lot of data off of those graphs.