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Ch2 part f Graphical Representation of Uniform Motion

Added Aug 27, 2018 •

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Chanello's take a little bit of a different approach to the idea of motion instead of looking at the algebraic and you sort of solving word problems let's take a look at the the graphical way of approaching the problems uniform motion then and what kind of information can you get your clearly there are sort of two kinds of grass that we want to look at it first as the displacement time graph for the distance time graph and then also the velocity time graph so let's start the simple displacement time graph Android compare that at the same time to a velocity time graph so it'll put time down here horizontal axis on the vertical axis we will have X displacement or V4 velocity now that could be a little confusing I do realize you know the x axis is the horizontal axis but remember the x-axis is a mathematical way of thinking about these graphs you're talking about the physics in the physics X represents the displacement or the position of the object and so for that reason we're going to be graphing of the variable in physics that we call X on the y-axis that they can a little confusing but I think you'll get used to it pretty quickly and recognize when you have that access is always going to represent for us the displacement or position of the object at some given time now our case if you think about the grass that we're looking at we want to look at something that provides uniform motion and a graph providing uniform motion means that this graph is going to produce a a straight line okay no change and no point will the line go steeper or more shallow or flatten out or go vertical it will stay nice and straight okay so what you can't see is that for every interval of time for example if I choose some interval of time then what I find is that the does increased by a certain amount over that time if I pick that same Universal interval of time but I will find that the amount that the displacement is changed by is the same as long as I pick the same interval of time another word for example if I pick 2 seconds then the amount of distance that I would travel if it were 10:10 here then for 2 seconds down here I would have also travel 10 meters here to remember vertically represents the placement does me something in meters or kilometers or centimeters and on the bottom is the change in time which would be in seconds minutes hours or some other unit of time important thing to recognize about this displacement time graph is that you can obviously tell what the displacement of the object is at any given time you could also look at the change in displacement so recognize that this change is doubt that down here is delta T so I can get the displacement in it at any time I can get the change in displacement at any time but more importantly I can also get another property of the of the motion of the object by doing a little deeper interpretation instead of Simply reading off the graph or just looking at changes in the value I can also calculate the slope of this line and think about what the slope of this line would represent I'm sure everyone knows that the slope of the line in simple terms is the rise over the Run and that would be the change in the Y variable over the change in the X variable and a guy I realized it's a little confusing because this actually is the math way of thinking about what x represents X represents the the horizontal axis but for us if we took the change in the y axis that would be are change in displacement if the change in the horizontal axis Delta X that would be the change in the time and I'm sure if you don't even need to flip back in your notes to recognize what the in displacement over the change in time represents of course that represents the velocity so extremely important to recognize that the slope of the line the slope of the line on the displacement time graph is actually the velocity of the object that's what that's a little deeper interpretation of a motion graph that we have not seen before that you may not have done a lot before turn your math class you calculated the slopes of lines but you might not have ever thought of the idea that the slope of the line might actually have physical meaning it might mean something in the real world and this case the slope of this graph represents the velocity of the object the object obviously being in back in the real world that looks translate how this graph looks into what would the velocity time graph look like how would the velocity time graph, when its shape be well obviously we're talking about uniform that is to say the object is not changing its velocity so because this is a graph of velocity versus time and we just said that I've lost is not going to change what we would be looking at is something that looks more like a horizontal to repeat the velocity was not changing so an object traveling with constant velocity would have a VT graph of velocity time graph that looks like a horizontal line the slope of the sign actually does have meaning also but we're going to get into that until I can a couple of extras from now when we start talking about acceleration for right now we want to look at another property of this crap so obviously just like with the displacement time graph I can read off the values from the scrap I can tell you the velocity at any given time I could tell you the change in velocity if I calculated the change in this case there is no change in the velocity or zero change in velocity but I can ask forget the displacement off of this graph so take a look at this trick if we sort of Imagine putting a dashed line here and we were to think about the area underneath this line what was the area represent of course I'm sure everybody knows that the formula for the area in this case we have a length times width let's take a look at what the length and the width are so the length in this case is velocity of the object and the width of this graph is the time and I'm sure you don't need to look back in your graph to recognize that the length times the Travelocity times the time would be abused the displacement so let's try to summarize real quickly cotton from the two graphs and then again we're trying to look a little deeper grabs when Rodger simply reading off the values of displacement sore velocities or X over trying to go a little bit deeper and look at it really two main things that you will do with graphs and that is to look at the slope of and look the area of the graph now in this case the area of this graph doesn't give us anything because of its shape it's simply because we have no formula so far and 1 * displacement the time / time we never multiply the two so the area of this mathematically it exists you can calculate the area of this crap it does exist it just doesn't mean anything physically and that's a tricky thing sometimes the area or the slope of a math mean something and other times it doesn't mean anything and you really have to look at the equations that you have to try and figure out does this actually have physical meaning or is it just essentially giving us some mathematical term that doesn't really mean anything in the real world to point out is that if this line had been moved up so say we have moved it up to here I would have the same velocity and my calculation of the slope would have been exactly the same what would have been different is that I would have had a different state position or initial displacement so let's try that so here's an example where I have an object moving at the same velocity but starting at a different opposition this would be asked not here's the trick when I go from this graph this motion of this object over here to the velocity time graph the velocity time graph would not look any different remember over here the velocity was represented by the slope and the slope has not changed so it's really crucial to recognize that I can draw an infinite number of parallel lines here I would not change what the velocity time graph looks like whatsoever that's a little bit of a tricky thing as that the velocity time graph can only show you the change in displacement cannot show you where you started he can only show how much you've added to whatever your starting point is so in a situation like this where you were given a velocity time graph if you were asked the final displacement you would have to be told in the text of the problem what was the initial displacement of the object how to figure out where the object is at the blossomtime graph is it has limitations in that it can only tell you how much you have added to the to the initial position or initial displacement so to little do you know mission of the Velocity time graph still very useful but it is a limitation of that that particular graph look at some examples I will look at our first example and putting some simple numbers so we can make the calculations and you can sort of see how this looks so we'll do a place time graph for both my farts acts here and this will be X in SA meters and time in seconds Travelocity 5 meters per second can I say for example that we're going to travel for 5 seconds as if you want to figure out how fast this object was going we would simply need to to calculate what it's the slope of the line and the slope of the line would give us the velocity so in this case v is equal to Delta X over Delta Chi and that would be equal to in this case calculating the slope it's 20 I'm going to take that point and that point to calculate my slope so I would take 20 - 0 / I look at my horizontal axis that would be 5-0 and I find it the velocity of this object is 4.0 April 2nd okay how does that look on the velocity time graph well on the velocity time graph we have the same 5 Seconds W determined that the velocity of the object was 4 meters per second and that would look like a horizontal line and what I can get from a lot of time graph is the displacement of that object at 5 Seconds how far has it traveled and that would be that Delta X is equal to v x t that is to say Delta X is equal to 4 X 5 Seconds which is 20 exactly what I got from the previous graph over here I got the same displacement as I get over here. Just to remind you this happens to be the final displacement only because my initial starting point was at 0 so when your starting point is zero then obviously the change in displacement or just simply the final displacement would be the same value 20 if I live right started a different point then I would have to figure out what my final displacement High finals basement was by simply adding it to the initial starting point

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Ch2 part f Graphical Representation of Uniform Motion

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