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Ch 2 part c Speed vs Velocity

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so now we have a little bit of understanding of how to make measurements of the the change in position of an object we can look at the distance of the object travel we could look at it it's displacement we could look at the change in displacement feel a lot of tools and belt in terms of thinking about how things have moved from one location to another bunch of different ways of observed analyzing their Motion in terms of these two new properties called distance and displacement so now let's actually talk about the motion that sell the only thing about the ocean musically going to be referring to either the speed or the velocity of the object and the way that distance and displacement were related to each other speed and velocity are related to each other through those definitions of distance and displacement definition of speed is the rate of change of distance now when it is simply stated as the rate of change its implied that it means per unit time that is to say that is the rate of change of distance as time is going on it's time as movie what time is Flowing now in case of speed since it's based on distance and distance was a scalar property that means its speed is also a scalar property that means that it's always positive now the letter that we choose speed and velocity is the same letter and I hope you recognize we can't use the letter s because we've already used the letter s to represent the distance so we cannot use the letter s to also represent the speed so we do is we use the same letter for both speed and velocity and that is the letter V show speed being the rate of change of distance that would be the distance that you traveled per means divide Sophie would be the distance over the time also sometimes see be over to you that's very common notation so they said depends on the textbook some books will use the letter D other books prefer to use the letter s if it's a very relatively high level if it's somebody's going on to be a physics major or to be an engineer but probably going to use  because calculus it turns out that in calculus the Hardy actually represents one of the mathematical operators in fact it's really the major mathematical operator in calculus and so is resulted at 10 and on Tuesday if they're books for people who are going to go on to use couch in our case with this is a non calculus based class so we may occasionally from time to time use the letter D to represent time and really important to know that since this is a scalar property this is always positive is never a negative proper velocity has a very similar definition it's also a rate of change per unit time but in this case it's the rate of change of displacement and remember displacement usually is not the same as the value of the distance it's not impossible could be the same they could be the same the distance that you travel in the change in displacement but really important to notice that it's the change of displacement is the change in distance that's what speed and velocity are based on in order to separate this be from that V we use what is commonly known as the vector hat notation you can actually draw just a regular Arrow so you can drop both sides of the arrowhead but generally speaking you'll see in MO books that they draw sensor like a half Arrow and that symbol above means that this is the vector version of it so speed and velocity are very closely related to each other and to separate the two we put the vector symbol over V in order to indicate that it's the velocity version of this and rather than the speed version now the equation is a little bit different because remember s is for distance instead of us since we're talking about the rate of change of displacement and it's the change in this place we would use Delta X over delta T so this is our are formulas actually put a box around these two formulas can up you also what we could do is essentially to sort of expand the equation by saying that V Vector symbol is equal to X minus X not poverty or that is to say we could solve to say that X was equal to so my final displacement is equal to v x t v x t will give me my change in displacement look back over here if I take the delta-t and I put it up here I could v x delta-t and what does that give me if I multiply the velocity times the change in time I get the change in displacement so the VT part is the change in displacement so if I add the change of displacement to my original displacement than that would tell me where my final displacement is is located at they're all the same question these are all the same there's no difference it's just a matter of which variable are we looking for Just Pizza formulas written as V is equal to Delta x / delta T you shouldn't think that it's always about solving for V of course not we can solve for did the change next week's top 40 we can even solve for either the individuals I can solve for the final displacement or the initial displacement for the change in displacement it really depends on the problem and what you're being asked for in some cases it's advantageous to have the change in displacement other times I might look for the actual final placement or be looking for the velocity or the or the time and similarly with the speed equation since we have the two equations let's take a look at an example that would allow us to analyze both of the emotions can somebody travel Who somebody I'm sorry who is 35 km north of the origin let him travel 55 kilometers to the south then head back 75 kilometers to the north and will complete this entire trip in 2 hours so let's start looking at the origin and will put somebody 35 km to the north Let It Go and we will have this person travel 55 kilometers to the South 85 km to the South would be minus 55 and then from that point I'm a put it out here to the side so it'll be a little easier to see while having travel 75 km back to the north okay so we started north of the origin but we traveled south by 55 and then traveled 75 back to the North and the question is asking for both the speed and also for the velocity of the trips a little start with speed sulfur speed we're going to need to know s the distance and in this case the Third time is irrelevant because that's his initial displacement what we want to know is when they started moving how far do they move so he traveled 55 to the South 75 to the north and really important to remember these are always positive distances distance is always it doesn't care whether you traveled North or travel south east west north or south it's all positive when you're thinking about the speed because again speed is based on the distance and distance is always positive so speed gun shy the distance for this guy is 130 kilometers the time now one of the things you're going to see you need it may seem kind of sloppy technically the equation sorry let's go back up here is delta T the change in time however let me point out that if no time changes then obviously nothing has happened so it's a little sloppy technically we should write delta-t every time that we do we do what the time it's very common among physicists and you'll find mathematicians think the physicist are a little bit lazy because we often times drop the delta-t off it is actually delta-t but we drop it off because obviously if no time goes by then we have no problem so just to make the notation a little bit simpler a little bit cleaner and I have to carry that delta-t around all the time you'll notice that when I drove wrote it up here I I didn't write the delta-t all the time just equations a little easier to deal with often times we don't use the delta-t because it's implied that when we talk about time that obviously Time Has Changed it's on this case we want to look for V without the vector symbol me without the Victor symbol would be  over tea and so in this case it would be 130 divided by 2.0 actually not going to write the the units cannot write to Eunice when I'm solving the problem because it just makes the algebraic algebraic cluttered and The crucial thing is just to make sure that when you go with me and that you get the right units for this guy so in this case we would be 65 and our units for this would be kilometers over hours so that's kilometers per hour and that's her final answer okay top RBS about the velocity how much do Part B underneath here so in this case I want Delta X don't you really noticed that when I was calculating the the distance to in order to get the speed I looked at the 55 and the 75 now in the case of the change in displacement I don't really need to look at those too but I need to look at is where was I at the end and where was I in the beginning so you know that this is going to be X-Men that's not so the final displacement and the initial displacement will the initial displacement I know that's really easy that was + 35 + so then minus sign comes from the the formula to subtract positive 35 but I need to know is where was I in the end so let's go back and take a look I started at 35 I went 55 to the South so at this point I'm now at negative 20 then I traveled 75. the north so starting from -20 and traveling 75 to the north is going to put me at plus 55 so we can write + 55 here and that gives us a change in displacement of 20 km now one thing that has not changed is the time was still the same no matter which one that we looked at so that's 2.0 hours I am looking for now the velocity not the speed so in this case I'm about to the right here is equal to Delta x - / delta T sorry so that's going to be 20 / 2.02 give me 10 kilometers per hour and that's our final answer

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Ch 2 part c Speed vs Velocity

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