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Find the displacement (in mi) on the time interval [0,2] and [2,3]. NOTE: displacement is net distance from starting pointFind the distance traveled over the interv...

Question

Find the displacement (in mi) on the time interval [0,2] and [2,3]. NOTE: displacement is net distance from starting pointFind the distance traveled over the interval (0.31 NOTE; distance Ine total dsuance without regard direction.Page 30/ 6

Find the displacement (in mi) on the time interval [0,2] and [2,3]. NOTE: displacement is net distance from starting point Find the distance traveled over the interval (0.31 NOTE; distance Ine total dsuance without regard direction. Page 30/ 6



Answers

On the graph below, what is the total distance traveled during the recorded time interval? What is the displacement?

Question number one In the given graph, we can see that there is no change in that direction. Off the motion off the person and this is position. This is time be. Since there is no change in the direction of the person and the distance off the person from the original position is increasing continuously. So we can say that that distanced every day is equal to the magnitude off the displacement. From this graph, we can see that the original point is that 1 m and the final point is a six meat that so that the stands Trevor it will be 5 m big is equal to 5 m and this is also equal to the magnitude older. This place man, this 5 m answer.

Discussion covers the concept of the displacement from the from the velocity time graph. Other displacement is the area under the velocity time graph. And from the given data, the initial displacement is zero. So if we want to calculate the displacement then we need to substitute time on the time axis. Let's name this point as Stephen where the velocity changes from negative to positive. Okay. And the time at which the velocity ins just name it tears. So from 0 to t even the velocity is negative. So the area under the graph will be the green area. So at any time t the area will be or the displacement is we In two G with a negative sign. Okay. Had time to even the displacement is minus of V. Time steven and after it even the displacement is minus of wheat even plus the this area this name is marty uh Plus the velocity V times t minus Stephen. Or the total displacement is Uh we T -2. We chiba if we draw the graph for the displacement and the time this is time and this is the displacement axis from zero to to even the velocity is negative. And from the situation the displacement is uniformly decreasing along the negative direction, Okay? And at times even the displacement changes direction and it goes towards the positive side. So it will both like this. This is T. F. And this is T. one. So this is the graph of a displacement was

Open number 25 r p is equal to the square off I plus 1/3. April 3 off. Jane Ah A T is equal to one. R is equal toe. I pass 1/3 Jane. At these April puts a being R is equal to nine. I last nine. Nine j So dente R is equal. Toe is equal to eight. All right. Plus 26/3 Jane S O r. Dash off the is equal toe to tee off. I lost e squared off. James eso The lure off our dash is quinto duty square the first piece where eso is equal to four teas workflow steep for four, which is equal to the square root off Oprah. Steve over to so s is equal to integration from 1 to 3 off the north off our square which is equal to t is square root off rusty square E t. Which is equal to ah times 2/3 four. Plus these were 3/2. So institution from one over trees. A final answer will be 1/3. The easiest way route off. 13 minus five. Squared little five

Okay, So this question we have to find the right dream on some with six of intervals. The left re want some with six up intervals and the midpoint remind some with 37 troubles on and were given a data table that tells us everything we need to know about dysfunction in order to calculate the re mance. Um, so the first thing I like to do for remind some questions is to draw a diagram. So, I mean, the intervals are gonna get a little bit different for each part of the problem, but we can use the diagram for all parts. So sorry. Um, so are Interval is from 0 to 3. So I'm gonna have a zero right here and three here. Um, and I'm gonna draw it with 6 70 role since two of our parts are with six. Um, so we know that these intervals are going even and they're given to us in the data table. So, you know, we're going to going up by 0.5. So 123 456 Um, so this is 0.5. This is one 1.5 two and 2.5 and I'm just gonna draw on arbitrary function. Doesn't really have to matter data just, you know, kind of to visualize What what's going on? Um, And were given what? The velocity is at each of those points, so we can just right. Oh, we can just write that out here. So you have zero 12. 18 25 20 for thine and 20. Okay, so now that we have this, let's do the right. Reminds them first. So we're doing this with sticks. Seven trebles. So, uh, here we're getting the height from the right side of the rectangle. So in this case, we're gonna be getting the height right here. So for our first rectangle, if we imagine a drawing like this, I'm not gonna draw them all because we have different ones for each part of the problem. But right here, we're gonna have 12. So we have 0.5, which is our Delta X or step size. Um, Times 12. Plus you to you. Plus 25 plus 20 plus 14 and plus 20. If you work that out, that's gonna be equal to 54.5. So 54.5 feet. Okay, Now I see the left rear lights on. So for the last three months, um, with 67 troubles instead of getting the area from the right side, we're getting the area right here. Or a misery. The height here, reading the height from the left side to find the area of the rectangle. So we're actually doing this area right here. Okay. So, similarly, the step size Delta X is your 0.5. Um, And instead of having 12 here, right and have zero plus 12 plus 18 plus 25 plus 20 plus 14 s a notice. We're not going all the way up to 20. This last rectangle would look like this, so the height would be 14. Okay, so now when you work this out Ah, you get 44.5, 44.5 feet. Does you see a big difference? The right remind some in this case was an overestimate. And the left room on some is an underestimate. Um, okay, so I'll see the final part, which is a midpoint re mance. Um, but in this case, we're using 37 troubles. So is that having six like we do here? We actually have. So this right here is gonna be one of our rectangles. This is gonna be a rectangle, and this is gonna be a rectangle, Um, and our height is gonna be the middle point. So we just draw that right here. Soc! For this first rectangle, the height would be 12 2nd technical 25 the record and go 14. Um, so in this case are subsides is not 0.5. It's one, as agency is going all the way to one. So you have one times 12 plus 25 plus 14. Um, and when you add, you get 51.


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