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1) The figure below shows the position of particle versus time_ with each line on the vertical axis representing 4.4 Find the average velocities for the time interv...

Question

1) The figure below shows the position of particle versus time_ with each line on the vertical axis representing 4.4 Find the average velocities for the time intervals and indicated in the figure_mls (time intervalSubmutm/s (time interyal b) Submitm/s (time interyalSubmtm/s (time interval d

1) The figure below shows the position of particle versus time_ with each line on the vertical axis representing 4.4 Find the average velocities for the time intervals and indicated in the figure_ mls (time interval Submut m/s (time interyal b) Submit m/s (time interyal Submt m/s (time interval d



Answers

The position versus time for a certain particle moving along the $x$ axis is shown in Figure P2.3. Find the average velocity in the time intervals (a) 0 to $2 \mathrm{s},$ (b) 0 to $4 \mathrm{s}$ (c) 2 s to 4 s, (d) 4 s to 7 s, (e) 0 to 8 s. (FIGURE CANT COPY)

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'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'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's, uh, plight this concept to Arthur lost searches in here. We'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're moving backwards in position. But in this part of the movement, the velocity is bigger than zero. Because we'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's ve to always will be greater than the one miner'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'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'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'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's the final answer. Thanks for watching.

Hi in that question, we have a particle that is moving in one dimension according to this graph on the right. So first let this one dimension be the X. And here we have on the vertical X. As a function of T. And we have on the horizontal the time itself. And the first part were asked to determine when the maximum speed of the particle and how much is this maximum speed? So just by looking at the graph, we know that the slope of the distance or the displacement curve is equal to the velocity. So where the slope is the most deep, this where the velocity is maximum and here you can know that this happens Between -1 and one. This portion of the graph is the steepest one, which means the one with the greatest slope. It doesn't matter if this slope is a negative one or a positive one, but this is the maximum speed. Speaking of magnitude. So let's calculate this magnitude here. So the velocity is equal to the slope which is equal to delta X. Divided by delta T. So here we have at the end of the portion where at one The displacement or the position is at -4 and negative The position originally at -1 was for and delta T. Is just two seconds. So that's negative eight, divided by two. This gives us the value which is negative four m per second. And again this is the maximum speed. Speaking of magnitude not of direction because the negative sign here indicates the direction of motion which is negative. So now let's move to be And we were asked to complete the average velocity between -5 and five. so here at -5 the particle was at one on the x axis and At five the particle was at -1. So that average velocity is calculated by displacement over time. So it doesn't matter the tragic tree or the path that the particle has taken but only the start and ending point. So here the particle ended at negative one And the particle originally was at one and the time here is 10 total of 10 seconds. So the answer is negative To over 10 which is negative. Open to meters per second. And that's the average velocity. You'll know the difference when we calculate the average speed and party. The average speed is different from the average velocity because speed, we calculate the distance traveled over time. It doesn't matter where you stopped or where you begin. But the distance itself or the path you have taken is what matters here. So let's look at the particle. The particle was originally at one and then a particle moved until we featured four. So here let's make a one dimensional representation of the particle's motion. That's our zero here. So the particle was at one and then it reached out to four and then it starts to move in the opposite direction until it reached negative four. So here that's negative four and then the particle started to turned back again until it reached it negative one. So here We have a distance reveled of three and then we have another distance struggled of eight. From four to negative four And then from -4 to -1 which is again three. So the total distance traveled here is three plus eight plus three, Divided by total time, which is 10 again. So here that's 14 divided by 10, Which gives us the answer of 1.4 meters per second. And part D. Were asked to calculate the ratio Of the particle's velocity between two and 3 and between three and 4. So now we need we need to get the speed in that portion here and then in that other portion here we can see that the speed is different because the slope of the curve induced these two portion is not the same. So let's first calculate the average velocity Between 2- three. That's delta X. Divided by delta T. Delta X. Here The particle ended at -2 And originally the particle was at -4. And the time difference here is just 1/2. So negative two negative negative four, that's plus four. So the answer for this is to Divided by one. So The velocity here is two m/s. Now let's do the same. But between three and four again delta X divided by delta T. At four. The particle ended at -1 Negative the original position at three which was negative too Divided by time, which is 1 2nd here negative negative. That's a plus. So here we have one divided by one Which is one m per second. So the ratio Between the two velocities is just to over one. Finally in party were asked to deter mine When the velocity of the particle was typically zero. So the velocity of zero means that the slope is actually zero. So when we look at the graph we can see that this period here the particle's position did not change between negative five and four, so the particle's velocity was zero here and this happened also between one and 2. The velocity was zero and finally between four and five. Here the velocity is zero as well, so the velocity Velocity is equal to zero between negative five until four and also between one and two. And finally between four and five.

Here for all the parts were actually calculating. Average velocity and average velocity depends on the displacement, not the total distance, not the total distance traveled, but rather your position away from the origin at that point. So essentially, again, we're not calculating. Uh, we're not calculating. Total. That's the displacement traveled that would give us the speed with respect to time. However, here we're trying to say average velocity. We're trying to find average velocity and so we're going to be strictly off the displacement now. Four part, eh? This is simply the slope of the line. So this should be from the origin to a We can say that the velocity from O to A this would be equaling 10 meters, minus zero meters because we're starting from zero meters and then the change in time would be two seconds minus zero seconds. This is, of course, because we're starting at T equals zero seconds and X equals zero meters, and so this would be equaling five meters per second. So this would be your average velocity for party again Weaken. We're simply saying that the average velocities equaling Delta X over Dr T and for part B we can say that. Then the average velocity here, from the origin to point B Ah would be five meters now minus zero meters, divided by four seconds, minus zero seconds. And this is giving us 1.25 meters per second. Four parts. See, Now we have the average velocity from A to B and so this is equaling five meters, minus 10 meters, divided by for seconds minus two seconds. And this is giving us negative 2.5 meters per second. This negative signs simply means that we are traveling towards the origin from point A to part to point B four part deed. Now we have the average velocity from B e T e t. And so this would be equaling negative five meters minus minus five meters, Rather divided by seven seconds minus four seconds. This is gonna be equaling negative 3.33 repeating meters per second. So this would be your answer for a party and then finally four part e the velocity from essentially from 0 to 8 seconds. So from the origin to the final eight seconds, which would be the origin to s, this would be equaling zero meters minus zero meters again because that point f were actually at the origin. We're back at the origin. So if we're if we didn't move, if our displacement of zero, it doesn't really matter what our time is, because if our displacement of zero hour velocity will always be zero meters per second. So this would be your answer for party again. The average velocity depends on displacement. So if you haven't moved from the origin at the end of your path, you're gonna have a zero meter per second velocity. Now, this is not equal to the speed the speed average speed is then taking into account the path or the path traveled or the total distance traveled. However, again, the question is asking for average velocity. So we're only depending on the displacement. That is the end of the solution. Thank you for watching

All right. Where were we has to compute the average velocity for a particle given, given certain positions and the part of certain initial position. Certain frontal, bosom and time interval. So the particle For the first question, Christian A. The initial position in the position of the particle is equals zero and Article two seconds. So tickles here. The particle initial position is zero meters from the origin. The final position. It's a 10 meters and the time interval is two seconds before according to the definition of the average velocity in one dimension, which is the change in position, many brother. With the change in time, we have 10 meters overs over to sickens or five meters per second. For the next question, we were asked to to answer to compute the average velocity for from seconds to four seconds. And for this case, the display Zeman his is the 40 meters and the change in time is four seconds. Therefore, the average velocity is for four meters per second or 1.25 meters per second. For the next question, we want to compute the average velocity between two seconds and t equals four seconds. So the initial position articles two seconds is 10 meters. The final position is five meters for the average velocity is for I understand meters over for minus two seconds and this is equal to negative 2.5 meters per second. The next question is to compute the average velocity between equals four seconds. Antique rose three seconds before writing a lot. About the change in time is three seconds in the change in position is and is six meters minus five meters, which is negative 11 meters afforded the average velocity and wonder Benjamin you seek will do minus 11/3 meters per second which is equal to miners three. 23 3 meters in the next. The next question is this is e think the previous one was was from member stick it Yeah, the Reza When you resist De and then the next one is he for this one? We want to compute the average velocity between tickle zero Zerg on anti equals eight seconds. You cannot as a a T equals zero The position the initial position Physical zero an A T eagles a second The final position secret zero zero meters zero meters for average velocity is zero because the change in the displacement is there. The average there is velocity is your


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