refer-to-the-position-versus-time-plot-in-figure-2-44-for-the-following-questions-a-is-the-average-s

Question

Refer to the position-versus-time plot in FIGURE $2-44$ for the following questions: (a) Is the average speed for the time interval between points 1 and 2 greater than, less than, or equal to the average speed for the time interval between points 1 and 3$?$ Explain. (b) Is the average velocity for the time interval between points 2 and 4 greater than, less than, or equal to the average velocity forthe time interval between points 3 and 4 ? Explain.

Nathan Silvano · Accepted Answer

Okay, So in this problem, we have ah, lot off. Position versus time represents the movement of object or particle. We can see that this movement is similar to a horrible, horrible movement. So we can argue that this is accelerated movement and the problem wants us to compare if the average velocity let&#x27;s put it this way. The average velocity between the 0.1 and two are greater. Smaller are equal. Then the velocity between the points one and three. Okay, so let&#x27;s suppose that this movement represents a movement off the off object with constant acceleration. If so, we can say that the average velocity between two points is just hess off the lost much of the first point. Tell us velocity off this second point. Okay, so let&#x27;s, uh, plight this concept to Arthur lost searches in here. We&#x27;re going to have velocity of between points one into going to be feet one. Well, us too divided by two. And you are decidedly going to have if you want, plus victory divided by two. Okay, so first we need to understand that. Look into the graph. This part of the movement of the graph we have negative velocity view is it? Last stints Europe because we&#x27;re moving backwards in position. But in this part of the movement, the velocity is bigger than zero. Because we&#x27;re moving forward. That means that the average velocity here, this signal between view one and victory is going to be a minor sign because this too have opposite directions off movement. So if we suppose this we can say precisely that view one, let&#x27;s ve to always will be greater than the one miner&#x27;s Vetri because here we are adding something. You are here. We are taking something. So the answer to the first I tonight and a he is going to be great there. Then you won in victory and this tough process it&#x27;s too holds Even if the acceleration was not constant because we can still apply devil aas it eas were still be the same. We still have a positive velocity from 4.3 in a negative velocity for 0.1 and two. So the second item were we going to do the same The second item We need to come there the velocities off points Ah, two and four with the velocities of points three or four OK, so using the same tough process, we&#x27;re going to have velocity of two plus velocity or four divided by two. And here we have. They lost the gift. Three Poulos velocity or four divided by two. Same thing we have here. Philosophy between one and four is going to have a minor sign. So the velocity between the points one and two and four it&#x27;s going to be less than develops. The average velocity off the points less then the velocities off points. 03 and four. We can put actually smaller, smaller, smaller than the average velocity between 0.3 and four. That&#x27;s the final answer. Thanks for watching.

Mayukh Banik · Answer

so the draft will look like this is the time for second it goes four and 48 and then two hours. So that&#x27;s okay. So this step back for a second. This is time, the maximum without to be 16. So disease velocity on this is 16 meters per second and that time is in second. So 16 a and for it starts at four. So here&#x27;s the forest warrant at eight. The second point, this is to have so at 12 the next point on then 14 and 16 and then 16 then 14 to as eight for zero 94 and they didn&#x27;t eight. So basically what we have is if we draw a shred line, this is one section, there&#x27;s a second section. Then he stopped and then eighties, the slow section and then it is the fast section again. So here it is, speeding up from here, too there. And then it is slowing down from here to there and then from here to there it is speeding up again on the opposite direction. So this ease Jan second on that is 12 2nd so far. Tend to do have second it travels scene reverse direction between zero and toe acceleration between t equals zero and two will be the same as acceleration between to as no uh zero one and two. Okay, acceleration between zero and two. Second with the but change in velocity would be 12 minus for major for second, divided by two seconds. So that comes out to be four meters per second squared and the acceleration from D equals G equals seven 2 12 2nd is just the negative off the previous acceleration with his negative four meters per second square just that it is in the opposite.

Jayashree Behera · Answer

the madam occurs, we have given our ex a witch&#x27;s Edo X is TV done. XY is goingto be nine. Me don&#x27;t nine months in Seattle, Time to travel. Toby is one second for saving his five seconds. Now, for the first part, we have to find the average velocity it is given by on the change in displacement or displace that the shortest distance traveled All my in fact. So for it to be me average is X B minus X over thinking bee minus t it. And this is a good maitre over one seconds because x a zero and zero. Come on. This little Logan&#x27;s out, Toby, to meet a close second from the scene. The ever it is XY minus experience over three C minus Davey and this is a little $6 over four seconds. And this could come slow toe B, 1.5 meters per second. Similarly, for it, you see average. Is this placement from seat away said he found it. Two c. It&#x27;s this&#x27;s both basically the same. So it doesn&#x27;t matter how you see this is a 19 year old five seconds. This is called the one on the second Now for the second part, the velocity is always in the same direction. Mattis. Positive ex direction. So the distance job is equal to displacement. In each of the case, on the average speed is same as the magnitude off the average velocity. So these two are bars physically present the magnitude ofthe the average velocity.

Efren Serra · Answer

for this problem over need to do is use the definition of the average velocity as it is the ratio of the change of the display. It&#x27;s been over the change in time and redivided from the graph. The first question was there was velocity from zero certainty two seconds from 0 to 2 seconds. The displacement is 10 minus zero meters, so the average velocity is five meters per second for being we&#x27;re supposed to compute the average velocity between the times off equals zero and equals four seconds. This place money&#x27;s fine money zero meters or were for China zero circles. And this comes out to me more important to five meters per second for C. The average velocity is supposed to be computer within four within two and four seconds. So there is never We&#x27;ll also is this bluesman over the Delta T And this comes some theories. About 2.5 There&#x27;s Persik, um, and for the you want to know between the times are four and seven seconds and the displacement is five minutes five meters. But as I said, when it&#x27;s four seconds or minus 10/3 years per second, which is a good. 23.3 years per second. Okay, Bonus. 3.3 meters per second. And then the last question E once is to compute the average velocity between t equals zero and equals eight seconds. This, please. 10 and the changing times a second. So there was a teaser.

Keshav Singh · Answer

So here we need to calculate the average velocity and the average velocity Define by the change of position Doctor X in the change over the change in timed out teeth and we know that x two finest x one over t two minus t. What so initially got two x is 10 meters and this time is two seconds on the average velocity for that journey is five meters a second. Now we do the same for the rest of problems. So again, the average IHS don&#x27;t x I doubt cheap and in this case, change in position is five meters any time for four seconds and hence we get the average velocity to be one 0.25 beaches the second so as we can see the average velocity changes for each part of the journey. But Potsie average velocity again. It&#x27;s too minus 61 over t two minus t one and thats final position is five meters. Find this initial position was it 10 meters over final time of four seconds minus initial time of two seconds and hence we get average velocity, which is negative since the direction of motion that&#x27;s changing and that&#x27;s minus 2.5 each is the same. So the negative science tells us that the direction is opposite to the initial direction of motion or D. We do the same again. The average velocity X two minus X one over t two by in this T way and here Finalist basement is my five meters minus starting point. Excite me just on a change in time, seven seconds minus and that gives us average muscle to you. You might, as three for me meters per second. So again, that&#x27;s opposite direction. Off initial motion. Finally, the average velocity off the entire journey again. Final position minus the initial position over the change time. But the final position is the same as the initial position. And so there is a lot of displacement is zero. Even though the time you take for the journey, it&#x27;s not against the average velocity for this journey is, you know, meet us the second

Averell Hause · Answer

you have an equation for position with respect to time in this case, So we can say for part A we have time equaling one second so we can plug in. Then we can say ex At one second, this would be equaling. 23 multiplied by one second, minus four multiplied by one second quantity squared plus one second quantity cubed. And this is giving us zero. So at one second we are at the origin. Four parts be. We have t equals two seconds and we can say ex at two seconds. This would be equaling three multiplied by two seconds. Minus form won&#x27;t. Supplied by two seconds. Quantity squared plus two seconds. Quantity cubed. This is giving us negative. Two meters, four parts. See, we have teas equaling three seconds. And this would be except three seconds giving us three times three seconds. Minus four multiplied by three seconds. Quantity squared plus three seconds quantity cubed. And this is equaling again. Zero meters and we have. Then we&#x27;re putting the weaken say ex at T equaling four seconds. This would be equaling. 23 multiplied by four seconds minus for multiplied by four seconds. Quantity squared plus four seconds Quantity cubed. And this is giving us positive 12 meters. And we can say that for part e, the position at T equals zero seconds. Of course, zero meters. And so the displacement between Teeples zero seconds and t equals four seconds. We can say that the Delta X would be equal ing x at four seconds, minus x at zero seconds giving us 12 meters and then finally for parts, we can say the position at T Will&#x27;s two seconds is subtracted from the position at T equals four seconds. So we consider displacement between two and four seconds would be ex at four seconds, minus x at two seconds. And this is equaling 12 meters minus negative two meters giving us 14 meters. And so the average velocity here would be equaling again. Delta X divided by Delta T. So this would be 14 meters divided by four minus two seconds. So four minutes to two seconds giving us seven meters per second. So that would be your answer for part F and then to four part G. It&#x27;s asking us to graft X versus T for 0 to 4 seconds. And as a quick sketch we have for a graph here. Here we have tea in seconds X and meters and we can say 2468 10 12. And then here we have we can say 1234 So we started the origin here. We make it too. A bit past one second. Where we Because at one second rather we have zero. So we&#x27;re basically just going to plot these? So one second is that zero and we have then at three seconds were also at zero. And so we&#x27;re going a bit up here down here and then from 3 to 4 at four seconds, it goes all the way to 12 meters. So it goes up, down, and then this large increase here where then, what we&#x27;re trying to find in part f would be two seconds Tau four seconds. So two seconds to four seconds. So this dash, the line would represent the slope of this. The dashed line would represent the average velocity from four seconds too, Uh, from two seconds to four seconds. So you can say slope equals average velocity. So I&#x27;d be your answer for part G. That is the end of the solution. Thank you for watching

Problem

NASA operates a 2.2 -second drop tower at the Gle…

Problem 95 Hard Difficulty

Answer

(a) Greater
(b) Smaller

Related Courses

Physics

Related Topics

Discussion

Top Physics 101 Mechanics Educators

Elyse G.

Andy C.

Zachary M.

Jared E.

Physics 101 Mechanics Courses

Math Review - Intro

Algebra - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 2

Video Transcript

James S. Walker

Physics

Elyse G.

Andy C.

Zachary M.

Jared E.

Math Review - Intro

Algebra - Example 1

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

(a) Greater(b) Smaller

Physics

Elyse G.

Andy C.

Zachary M.

Jared E.

Math Review - Intro

Algebra - Example 1

James S. WalkerPhysics

Elyse G.

Andy C.

Zachary M.

Jared E.

(a) Greater
(b) Smaller

James S. Walker

Physics