 We're going to talk about what happens to things when they're undergoing constant acceleration now, and things undergo constant acceleration all the time around us, provided air resistance is negligible, because that's what gravity does. It took a long time to realize that air resistance was an important feature of falling things. Aristotle used to think that heavy things just naturally fell faster than light things. Which looks like a reasonably good result of that experiment. But it's not necessarily the heavy thing and the light thing acting differently under gravity there, because he didn't think about air resistance. Galileo put forward a thought experiment that made Aristotle's idea that heavy things fall faster than light things seem a little strange. He said suppose you have one cannonball and another cannonball exactly like it. So because they're the same, they'll fall the same. Now if we had a bigger cannonball instead, you'd expect that to fall faster according to Aristotle, because of gravity. Now suppose you have those two cannonballs, and instead of having one twice as big, we just had those two attached by a little chain, like just a tiny little hair. That's now a bigger thing, right? So when I drop it, it should fall faster. But we can know that if we attach two cannonballs by a hair, that's not going to change how fast they fall at all. So that goes against our intuition. Oh, well, says Aristotle. Okay, you have to make it thicker. They have to be properly attached. Right? Well, how thick does it have to be? Does it have to be just a rigid little chain? What if I put a tiny drop of glue between them? Do they suddenly fall faster now? That doesn't really work with our intuition either. And in fact, what we understand now is that air resistance is really important in understanding why heavy things seem to fall faster. If I have my piece of paper, then it falls. It's falling because of gravity, but it's also being pushed up by the air. And the main reason that this pen falls faster than this piece of paper is because of the air resistance. And you can test that by taking the air away. And then when you've got no air resistance, you see that these two things will in fact fall at the same rate. Well, in my left hand, I have a feather. In my right hand, a hammer. And I guess one of the reasons we got here today was because of a gentleman named Galileo a long time ago, who made a rather significant discovery about falling objects in gravity fields. And we thought that where would be a better place to confirm his findings than on the moon. So that's got to be absolutely the world's most expensive version of that experiment ever. And yet it wasn't even in HD. You get the same effect just by putting things in a vacuum tube and sucking out the air. Now Galileo didn't just think about gravity and say, I don't think Alice Dottel can be right. He actually went and did the experiment. And when he was doing the experiment, he didn't have really great clocks and things fall pretty far. So it's hard to get accurate time measurements. So he slowed things down by putting things on a slope and rolling them down the slope. He tried different slopes and he found that indeed gravity caused things to accelerate at a constant rate. So to keep things simple, we'll just start by considering motion in a single direction. So we have some object that's got a position we can define and it's traveling in some direction. It's really important in your diagram is to be as clear as you possibly can. And so we're going to have a before diagram and an after diagram. And you'll note I've explicitly said after a time t for my diagram, so I've kind of defined my symbols in my diagram and that's good practice.