Problem

A stone is thrown horizontally at 30.0 $\mathrm{m…

05:39

Problem 5 Medium Difficulty

Q. An athlete starts at point $A$ and runs at a constant speed of 6.0 $\mathrm{m} / \mathrm{s}$ around a round track 100 $\mathrm{m}$ in diameter, as shown in Figure 3.35 .
Find the $x$ and $y$ components of this runner's average velocity and average acceleration between points (a) $A$ and $B,$ (b) $A$ and $C,$ (c) $C$ and $D,$ and $(d) A$ and $A$ (afull lap). (e) Calculate the magnitude of the runner's average velocity between $A$ and $B$ .Is his average speed equal to the magnitude of his average velocity? Why or why not? (f) How can his velocity be changing if he is running at constant speed?

Answer

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Physics 101 Mechanics

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December 9, 2020

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Video Transcript

given the diameter off the circle, we can find the radius using the half off the diameter. So this is going to be 50 meter. And using this value ofthe videos, we can mark the components off Evie City. As so it will be minus har co Macedo coordinates off Leap, baby baby Ciro Less Seo less Taj saves sees going. Toby AJ Segal Andi will be given by the points Teo and art on were given the tangential velocity. Uh, so velocity at each point on the circle is going to be a tangent. Abandon ship in tow. The part at that point. So these are going to the direction of velocity at which all this points and since the magnitude is gone, stoned began Mark the confidence of velocity. Yes. So it cited him. Do koala set point A. This is going to be CTO. I mean, my point being this is goingto believe Zine cto Similarly, 4.6 will see you minus v on that, Dean, this's going to be minus Please you. So if you're confused about how I used the velocity, let me just repeat again. So the direction off velocity at point a is upward on. There is no component off velocity along X direction. So velocity along extra diction, the competent of the lot stay along extra addiction. It's going to be zero on DH on the confident of velocity, and my direction is going to be V or six meter per second. And since the direction is upward, this is going to be positive. Similarly at point B. This is moving. This is pointing towards a positive X axis and there is no component of molesting all my directions of that is going to proceed or on DH. The exact says This will be given by you for seeing velocities downward and only in the white direction, negative direction. So ex company and, uh, velocity will be zero on my component is going to be AA minus three because after down outside and some relief appointed now, for the first part, we find, ah, the Valium for one loop, one full lap, which is the time taken by the particle toe. Make one full round off the circle. So this will be given by the total land or the total Sark informants off the circle. So that is going to be by God over the velocity, which is constant and is given by six meter per second. And this gives the timeto be 52.4 seconds. This is sometimes called as the time period because this is the time taken by the article to make one full drunk. So from here, Toby Ah, we see that this is just 1/4 lap. So from a to B, the time taken, that would be 1/4 off the total dying. So this will be then hurting 0.1 seconds. Now we can find the average velocity along except my direction. It's a long X direction this the people. And by changing the garden, it's off x over the time taking to move from the trapeze. So this is the basics. A minus x bean old vanish on that day it is. Do it. It's an X in Seattle X being Ah, OK, so just imagine it. This should be finer distance minus the emission distance. When we say don't like, they should be finalised ins, which is X B minus 60. So, yeah, now we can right X B. That is Siegel minus X A. This is negative. Odd and God is 50 meters or what they may be So the sausages and beget this value. Toby CCI Point In a couple seconds, we do the same thing for the wind direction. So this is going to be dead by overdone lt on Del. Why is Wybie my ex wife? Oh, right. Maybe. And this value is through on tape. Next we have to find the acceleration. So acceleration is average. Acceleration is basically the changing velocity over the time taken. So this is going to be the ex. Some bell, the X or wise then so from a Toby along extra diction we have We'll be in the extreme to be equal to V, which is six meters per second. The X A is Siegel Sandel days. The value that we can collected here just stick baby from this lugging that I lose, we found circus is V 26 minus Siegel Mitt off a second forward time. It's a starting point monster. This is it called a 0.6 Need a ballistic second Middle Signet's grand. We did the same thing for acceleration and my direction. So this will be there will be wind over Del so confident. All the light. Sorry. Accompanied of velocity along my direction. I find minus levi at point B, divided by eight. And this will be quite negative. Zero point. Poor six. Me dip a sick? No, this is the first part. Now, for the second part. You see that from 80 see, this is no half lap because it covers half the silk influence off the circle. So the time taken will be half off the time period, which is 52.4. So be is even being baffled. 50 to 14 seconds and this is equal to 26 point two seconds. Now we can find the velocity using the same question as they used before. Except this time the after use Hello. The coordinates at point C instead. Off point. This is a quantity 0.8 meters per second. Similarly fine, Mrs Quito. Then light nobody lt. And you'll see that this is equal to zero. Similarly, the average acceleration will be then the ex or weird. Lt This is being re X C minus Nick's age over being a C. So sometimes I'm writing liaising. Sometimes I'm letting this year, so don't get confused about their They're basically the same. This is a Cueto. Cedo on why I have edges. Go on. This is going to be called. No. Get syrup on for six meters per second. Now I'm pretty sure you must have. I got an idea about how the things are walking. So for the third part, we have to do the same thing Gone C o D. Which is again 1/4 lap. So be seating is basically one fought off the total time, and this is again going to be hurting 0.1 seconds Minutes. I do the things fast because now you have an idea off too. Uh, could these things done on the next? This is going to be CTO minus to me. Well, we're 13 going one second. The three point dates events, acceleration averages. So remember when you're dating the coordinates, make sure you're taking them corresponding to these two points. And always you might ah, get you don't got so that is toward by for the last part, you have to find from a tow A So that is one full round. Right? So he is going to be called to the time video, But since the particle returns back toe the original position, they'll x on Gail White are goingto zero, and so will be the ex Andi by at this put the average velocity along extraction and average velocity in my direction. So if you if we use those values to find the acceleration on the velocity, those are also going to because the serial, because telex, Then why does the X and they'll be going to prison? Let's just like all those values, something X And like I said, Oh, on DH. So this gives the ex average on DH the guy average to be quite a zero using this tone questions also then re X on delivery y our sio on this gives that average acceleration a long exam duration of zero for the fifth. But we have to find the magnitude ofthe the object's velocity. This is going to be equal to route over, off the some off the square off the components. This is for it to be so we're going to use B X and B by average, corresponding to these points that is goingto be despite because, yeah, so we lose these two values. So this is going to be going t 0.8 square. That's 2.8 square, and it's not writing the units to save some time. But when you do, the calculation makes yours. You taken off the units there, so the speed is gone stoned. So the average speed is six. Meet up for a second. Over here, the average speed is larger than the magnitude ofthe the average velocity because that because the distance traveled is larger than the displacement. So what I want to see is this is the average speed on the one we found. Here is the average velocity. Now, average speed is given by the change in distance over time. On average, velocity is given by displacement. Overtime and displacement is the shortest distance. So if you say from it to be, then the distance is visibly this ark like displacement, they will be basically the line joining these two points. So this land, the ark is obviously greater than the slime. And that's the reason, uh, the average speed the straighter than after its velocity. So I've answered, in fact, makes sense from the fifth flag. Ah, since velocity is a vector that put magnitude and direction. The magnitude ofthe the velocity is constant, but its direction keeps on changing. So that's right, baby, which is the magnitude which we found on the 5.4 meters per second. It's going to be constant with Tita, which is the angle needs by the velocity on the magnitude ofthe this velocity. The velocity vector with the exacts is he's going through teams Did Michelle. How so? At this point velocity the direction off velocity is going to be like this from they don't see This is going to be like this from C today. This is going to be like this and same for deed to a handful at the points.

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