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Anderson Video - Vector Kinematic Equations

Professor Anderson
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 >> Hello class. Professor Anderson here. Let's talk about the vector kinematic equations. These are the same equations that we've been looking at in one and two dimensions and now we just want to make it an arbitrary vector. How would we write this out? Well, the position of the particle, we've been using r for our position vector, okay. You can use whatever variable you want but I like r. What does r look like? Well, it is x i hat, plus y j hat, okay. It is some coordinate in the x component, some coordinate in the y component. You add them up as a vector and that tells you the position of the particle. What about the velocity? The velocity v is v sub x i hat, plus v sub y j hat and the acceleration a is a sub x i hat, plus a sub y j hat. If you have three dimensions you can add a k hat if you like, but two dimensions is usually plenty. Now, how do we deal with these kinematic equations in terms of these vectors? Well, r just becomes r f. On the right side, we have r i, we have v initial times t, and we have 1/2 a t squared. r f is a vector. Everything on the right is a vector. Vector r, vector, v i, vector a. And velocity we can write as the following: v f equals v i plus a t, okay. If a is a constant, then a is given by that. And remember, it's still a vector. Now, this is a nice way to write it, but remember what's in there is actually two equations in each of these. So, in the r f equation what we really have is an equation for x, x final equals x initial, plus v x initial, times t, plus 1/2 a sub x t squared. And we have an equation for y. y final equals y initial, plus v y initial, times t, plus 1/2 a y t squared. And in the v f equation we also have two equations in there. v x final equals v x initial, plus a sub x t. And v y final, equals v y initial, plus a sub y t. So any time you see vectors, remember that there are really two equations in there: x equations and y equations. Okay, any questions about the vector kinematic equations? Okay. Alright. Hopefully that's clear; if not, come see me in office hours. Cheers.