funding for an audible paint course television was made possible in part by the College Board almost nobody can reason with you Mr Wares Cunningham McHugh the great founder itself and all other funding were made possible by viewers like you we forced you [Music] oh hello welcome to another episode of the apctv the mechanics Edition I'm your host of Summer q and today you'll be watching season one kinematics episode 4 no graph about it so the objectives for today's video is to be able to describe the motion of an object based on its motion grab so a motion graph is a graph describing the motion of an object and when I say motion you say position velocity or acceleration x v and a so the first motion graph we're going to look at and analyzes a position versus timer and X verse T graph I mean look at these graphs it tells you the position whether it's a positive position negative position zero position and the slopes tell you the velocity so this first segment you have a constant positive slope which means you have a constant positive velocity and since velocity is constant meaning your slope you have no acceleration the second segment you have no slope which means you have no velocity and no acceleration your motion is constant you're not really moving at all the third segment the slope is increasing so you have an increasing positive velocity and in acceleration this is probably a constant acceleration but you know you have an acceleration because you're increasing your velocity this third segment the slope is now negative so you have a negative velocity that's constant because it's a constant slope which means you have no acceleration and this tiny part towards the bottom you have a decreasing slope which means your velocity is getting smaller and you have an acceleration so you have a decreasing slope which means if a decreasing velocity and that means you have an acceleration opposite the motion so if you were moving in the negative Direction with the negative slope and you're slowing down your acceleration is positive your V is decreasing that's shown by a decreasing slope on this position versus time graph so when you see position first time you can read it to find the position and read it to determine what the velocity is based on the slope and you can also think derivative slope derivative go hand in hand the next graph is velocity versus time and what this tells you is the instantaneous velocity at each point whether it's positive negative in the value and the slope will give you acceleration the area under the Curve will give you total displacement so again slope is acceleration think derivative with slope area is displacement think integral for area and that goes with the calculus episode where we said to get acceleration from V you take a derivative to get position you take an integral so on this journey of V verse T if you have a positive flat line for velocity means you have a positive constant velocity and since there's no slope on our V versus T graph you have no acceleration but then you have a v that's trending towards zero and whenever V Trends towards zero that means you're slowing down when things Trend towards zero it means you're coming to a stop so in the second segment we have a decreasing velocity and since the slope's negative we have a negative acceleration that happens to be constant when you cross this point I circled on the Zero line it means you change directions it means I was moving at 10 meters per second positive five meters per second positive I stopped now I'm heading the negative Direction moving down or in the negative Direction so whenever you cross that's x axis on a V verse T graph you've now changed directions your velocity is heading in the opposite direction and that's where you're headed and now we curve up and since the slope is increasing the acceleration is increasing so it really to break down these graph graphs ask yourself what has happened to the slope and what has happened to the area if slope is constant then acceleration is constant if slope is zero acceleration zero if slope is increasing or decreasing then acceleration is increasing or decreasing and the last one and there's not much to it is an acceleration versus time grapher averse t we typically only deal with two scenarios a constant acceleration that's positive a constant acceleration that's negative and I guess I'll throw in the third one if it's zero but when you're getting a verse T graph the only thing you can really tell me is if there's acceleration and the change in velocity so the area of an acceleration first time graph gives you change in v it doesn't tell you the velocity unless you start it from rent it tells you how much the velocity should change because acceleration is the rate of change in velocity so it tells you how much your velocity is change if you take the area meaning integral and if the graph reads A flat line you have a constant positive acceleration if it's on the top side if it's on the bottom side it's a constant negative acceleration and again there is the possibility it's also zero so if you have any questions you can leave them in the comments below or email me otherwise have a fantastic night