![]() ![]() So what does this look like? Well, I haven't proven it to This point correspond to? You're back at A. And then you'll startĭecelerating at that point. It's going to be reallyįast at this point. Your velocity is going to getįaster, faster, faster. And then you're going to startĪccelerating back. Point, right here, you start decelerating. So what's happening? When you start off, you're Pattern, right? And it'll keep going here and Of x is not constant, so you wouldn't have a zigzag Then you're decelerating this entire time. Think about it, you're actually accelerating atĪ decreasing rate. We know at this point you haveĪ very low velocity. Here you have a very high velocity, right? You have a very high velocity. That is that you would have a constant velocity, Means that you would have a constant rate of change It- if you have a straight line down that whole time, that Will it just be a straight lineĭown, then a straight line up, and then the straight But let's think about what theĪctual function looks like. And then at the points inīetween, it will be at x equals 0, right? It'll be there and there. It will have compressedĪll the way over here. To be the x position? Well at T over 2, the block To get here was also the same amount of time it Get here, right? The same amount of time it takes There and back, it takes T over 2 seconds to Get some intuition of what this function mightīe analytically. Points that I know of this function and just see if I can Time it takes to do that whole process, right? So at time 0 today, and then weĪlso know that at time T- this is time T- it'llĪlso be at A, right? I'm just trying to graph some And then do that whole processĪll the way back. Slowing down, slowing down, slowing down. It's going to accelerate,Īccelerate, accelerate, accelerate. It takes for this mass to go from this position. Graph is, right? Actually, let's do something So at time t equalsĠ, where is it? Well it's at A. Is A, right? So if I draw this, this is A. The x position of the mass? Well the x position Here, this is at time equals 0, right? So this is at 0. You know x is a function of time, x of t. That's because x is the dependent variable in This might be a little unusualįor you, for me to draw the x-axis in the vertical, but So let me try to graph xĪs a function of time. So let's just get an intuitionįor what's happening here. So let's see if we can just getĪn intuition for what x will look like as aįunction of time. The way, until all of that kinetic energy is turned back To keep it going, and it's going to compress the spring all Velocity and a lot of kinetic energy, but very little Gets back to its resting state, it'll have a lot of It's going to get faster andįaster and faster and faster. Is going to pull back this way, right? The spring is going to Restorative force of the spring, is equal to minus some constant, times the x position. Happen to this? Well, as we know, the force, the Have a mass, mass m, attached to the spring. ![]() That's where the spring's natural resting Like I've done in the last couple of videos. The world of differential equations a little bit. Learn a little bit about harmonic motion. Know about springs now to get a little intuitionĪbout how the spring moves over time. The final answer to your question is that you don't have to know calculus to learn physics but it helps. The physics that we're trying to learn in these videos was the motivation for the invention of calculus. This led to the concept of what we now know as an integral. (Keep in mind that Newton was inventing this math on the fly so the notation that we have today didn't exist yet.) Newton also noticed that for each derivative there was a corresponding sum from which the derivative could be obtained. This led him to develop tables of what we now know as derivatives. (At that point, a rudimentary understanding of algebra was all that Newton had and that was self-taught.) Newton took a break from his physics experiments, and scrutinized his results. Newton made all kinds of experimental observations of motion, but he didn't have the mathematical tools to describe what he was seeing. That said, solving physics problems of this sort is what motivated Issac Newton to invent calculus in the first place. That is why Sal avoids discussing the calculus whenever it is not necessary to the discussion. ![]() As such it is important for anyone to have a good intuitive understanding of physics whether or not they are good at math. Physics is the study of the way the world actually works. Sal is not emphasizing that calculus is tough so much as he is avoiding the use of calculus for the sake of not confusing people who don't understand it. ![]()
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