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Welcome to our math review video where we're going to talk about how the plots of derivatives and integral czar important in physics. Um, in particular. This is going to be, uh this is gonna be an instructive, uh, instructive video for those of you who are just starting out doing the first unit in physics because this almost always will show up. So what I'm talking about here is if I have a function f of X versus X, and I say, Okay, my function looks like this. And I say, Well, if I took the derivative of that, I would just get zero. If I took the integral of it, I would get some number. But what does it mean? Okay, in physics were really worried about What does it mean? Why would we apply this? Well, the reason we would apply it might be to say, if a knob checked is moving in this case, we might say, What if I have an object for which its position looks something like that? So we're plotting against t here. Eso its position looks something like this. And I say, Well, what if I take the derivative of that I've already told you that the derivative of position with respect to time turns about to be speed. Okay, well, the speed then we see we have a constant slope, which means we're gonna have a constant speed. Okay, so that's that's very interesting. Were able to go from the picture that we have for position down to the picture that we have for speed. Similarly, if I were to say, I have speed with respect to time and it looks something like this and say I want to take the integral from here Thio here. Well, what I'm going to do is when I take the integral from here to here, I'm going to get that much. When I take it from here to here, I'm going to get a slightly more amount. When I take it from here to here, I'm going to get more. And so it's increasing at a constant rate, which means that if it's increasing a constant rate than my position, which remember, position is equal to the integral of speed with over speed, with respect to time, then my position is going to be changing at a constant rate because we were as we took the integral. We got a standard increase. Okay, so this is this is kind of an interesting relationship here, and we can export more, and we will explore a lot more when we come to cinematics. So, for example, what if we were to have some chicken a metric functions instead? Stay. We have sign of X versus X, and I want to take the derivative of this well, so we remember it looks like this. And if I want to take the derivative of it, then I can see well, here, it's gonna be a maximum in positive. Here it will be. Zero here will be a maximum and negative. Here it will be zero, and I start to come up with the cosine function, finding that the derivative of sign will be cosign again, you might say, Well, where does this apply? Well, when we do Oslo Torrey emotion, we'll find that the position is described by a sign or a cosine function. And in order to find its speed with respect to time, will take the derivative and come up with either a cosine or negative sign. So, uh, the plots can tell us a lot and being able to look at a plot and figure out the derivative or integral of that plot just by staring at it can give you a lot of insight into what the answer to your question will be. I really recommend that you practice this with a couple of well known functions, things like Pollen Oh, Meals during the metric functions and exponential.

University of North Carolina at Chapel Hill

Motion Along a Straight Line

Motion in 2d or 3d

Newton's Laws of Motion

Applying Newton's Laws

Work