Position-time graphs | One-dimensional motion | AP Physics 1 | Khan Academy

What we're going to do in this video is think about different ways to represent how position can change over time.

So one of the more basic ways is through a table. For example, right over here in the left column, I have time—maybe it's in seconds—and in the right column, I have position, and this could be in some units. Let's say it's in meters.

So at Time Zero, we're at three. After 1 second, we are still at three. At 2 seconds, we're at -1. Then after 3 seconds, we're at zero. After 4 seconds, we're at zero—still at zero. After 5 seconds, we are at two—maybe 2 meters.

Now, this is somewhat useful, but it's a little bit difficult to visualize, and it also doesn't tell us what's happening in between these moments. What's happening at time half of a second? Did we just not move? Did our position just not change, or did it change and then get back to where it originally was? After 1 second, we don't know when we look at a table like this.

But another way to think about it would be some type of animation. For example, let's say we have our number line, and let's say the object that's moving is a lemon. So at Time Zero, it starts at position three. So that's where it is right now. And let's see if we can animate it. I'm just going to try to count off 5 seconds and move the lemon accordingly to what we see on this position-time table or time-position table: zero, one, two, three, four, five.

So that was somewhat useful, but maybe an even more useful thing would be to graph this somehow so that we don't have to keep looking at animation. So that we can just look at with our eyes what happens over time.

For that, we can construct what's known as a position-time graph. Typically, time is on your horizontal axis, and position is on your vertical axis. So let's think about this a little bit. So, time equals 0; our position is at three. So at Time Zero, our position is at three.

And then at time equal 1, we're at three again. At time two, we are at 1—at time two, our position is -1. At time three, our position is zero. So our position is zero. Remember, even though we're thinking about left and right here, position is up and down. So here our position is zero at time three, and then at time four, our position is still zero.

And then at time five, our position is at two—our position is at two. So for the first second, I don't have a change in position, or at least that's what I assumed when I animated the lemon.

Then, as I go from the first second to the second second, my position went from 3 to -1. From 3 to -1, and if we do that at a constant rate, we would have a line that looks something like this. I'm trying to—that's supposed to be a straight line.

Then from time 2 to 3, we go from position -1 to 0. From -1 to 0, here it would have been going from negative 1 to zero, moving one to the right, but over here, since we're plotting our position on the vertical axis, it looks like we went up. But this is really just going from position -1 to position 0 from time 2 seconds to 3 seconds.

Now, from three to four, at least the way I depicted it, our position does not change. And then from time four to five, our position goes from 0 to 2—from 0 to 2.

So what I have constructed here is known as a position-time graph, and from this, without an animation, you can immediately get an understanding of how the thing's position has changed over time.

So, let's do the animation one more time and just try to follow along on the position-time graph, and maybe I'll slow it down a little bit. So over the first second, we're going to be stationary, so we could just count off one Mississippi.

And then we go to our position—goes to negative one over the next second. So then we would go to Mississippi, and then we would go three Mississippi, four Mississippi, and then five Mississippi. But hopefully, you get an appreciation that this is just a way of immediately glancing and seeing what's happening.