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