>> Hello class Professor Anderson here. We're talking about two -dimensional motion and let's think about drawing a picture an x-y coordinate space of a particle moving around. So we don't know exactly what the trajectory is but we can just write one. Let's say it looks like that. Ok starts over here at point A goes to point B. Now if this is you driving around on the earth in your car what would the instantaneous velocity look like? Well, the instantaneous velocity of your car is always pointed along the direction that you're driving so if I wanted to calculate the velocity here it would be pointing tangentially to the curve. If I wanted to calculate the velocity there it would be in that direction, over here it would be in that direction. Ok so as you're driving in your car and you steer the wheel you are changing the instantaneous velocity vector of your car. Now what about speed? Speed is just the magnitude of that. Ok and if I look at this graph this Y versus X graph of the motion can I calculate the speed? Is that enough information to calculate the speed? What do you think yes or no? Yeah. >> No. >> No, why not? >> Because you don't have acceleration. >> Ok. >> If you use the kinematic equation. >> Ok. >> You won't have enough information. >> Alright. Excellent. Let's think about that for a second. He said if we use a kinematic equation and one of those kinematic equations looks like this he said we don't know the acceleration, which is true but we also don't know what the time is right. So this graph what we've drawn here it's just a map of where you've gone right? You started at A you went to B but it doesn't tell us anything about the time that it took to do that. We're missing information there. Ok and so somehow we need to get more information in our problem. One of the things that you just mentioned is the acceleration right and let's just define what we mean by that. Average acceleration, again, it's a vector but we just draw it with a bar on top is delta v over delta t which is v final minus v initial over how long it took. Ok, good. What about instantaneous? The instantaneous is what does this look like when delta T goes to a very small interval? So we write it like this, it's the limit of delta V over delta T. As that interval gets very small and that is of course the derivative. So what you need to know to calculate the acceleration is the velocity as a function of time and what we don't have here is any of that time information right? We just have position information so we need a little bit more. Now it turns out that all of the kinematic equations that we've talked about we can write in vector form so let's do that.