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Problem 2.27Acar slows down unlformly from speed of 23.0 n / t0 rest in 8.20Par AHow far did it travol in Ihat time?fo AEdSubmitRequest AnsworProvide Feedback...

Question

Problem 2.27Acar slows down unlformly from speed of 23.0 n / t0 rest in 8.20Par AHow far did it travol in Ihat time?fo AEdSubmitRequest AnsworProvide Feedback

Problem 2.27 Acar slows down unlformly from speed of 23.0 n / t0 rest in 8.20 Par A How far did it travol in Ihat time? fo AEd Submit Request Answor Provide Feedback



Answers

(II) A car slows down uniformly from a speed of 21.0 $\mathrm{m} / \mathrm{s}$ to rest in 6.00 $\mathrm{s}$ . How far did it travel in that time?

Here in discussion. You have given the diameters all those the diet equal to 80 centimetre. That means radius of Tire is equal to 40 centim. All we can write this as 0.4 media. Yeah. Also we have even that the. I asked Spence. So 23 points live rotation and 75 seconds. No, we need to calculate that. How far does the fab in travel in the in that lying during it is struck in the head of what? So for this first we are going to calculate that how much the stands the table travels in one rotation. So in one rotation distance. I love words why the devil will be even equal to rule. Why us Now on putting the values we get the even is equal to By my people about 0.4. So from Hubble we will get even is equal to you. 2.51 33 meter now and only three points five rotations. The Robin robbers. The distance D equal to 23.5 multi bye bye diva. That means d. is equal to 23.5. My people are by 2.513. See now after multiplication, we get B is equal to 59 point 062 media, all approximately Weekend c. 59 major. That means that the travel travels 59 major.

So we have a velocity, the initial equaling twenty eight, twenty point zero meters per second and then it's coming to a stop. So the final equals zero meters per second and we have a delta t of eight point zero zero seconds. So essentially here we have ah, uniform deceleration or negative acceleration. And it's asking us for how the distance traveled within this period of time. So we should first find the acceleration that's going to be Delta V divided by Delta t. We know that the final is zero. So this is something gonna be negative. Twenty eight divided by eight and this will equal negative three point five meters per second squared. So this will be acceleration and then to find out acts, we simply this is going to be able to be X initial t close one half eight, he swear, And then we can substitute directly so we can say twenty eight times eight plus one over two times minus three point five or negative three point five and then times t squared toe eight squared and this is gonna equal one hundred and twelve meters. So this will be our delta acts this will be how far we traveled in that eight second time interval. That is the end of the solution. Thank you for watching.

So the question tells us that a gyroscope is spending at 32 radiance per second, and it begins to decelerate at 0.7 radiance per second squared. And we're trying to find how long it takes for, uh, the gyroscope to stop spinning. And so the way to do this is by using our Kid Matic formulas, one of which states that the angular velocity is equal to the initial angular velocity, plus the angular acceleration times time. So we know the acceleration is 0.700 readings for second squared. And it's actually going to be negative because it's going against the positive, uh, radiance per second that we have here of the angular velocity, Um, and because it's slowing down, so it must be negative. And we also know the initial angular velocity is 32 radiance per second. In the final, angular velocity is going to be zero radiance per second because the gyroscope is going to stop. So if we plug all this in, we're going to have zero equals 32 plus actually sorry, minus because it's negative minus 0.700 times the time and then we can sell for tea and we'll see that T is equal to 32 divided by 0.700 And when we do this will find that the answer, uh, is equal to 45 point 45 0.71 seconds.

Okay, So the question want us to return me? How much time passes before the police car overtakes the speed? But we know the initial speed for the police car is 95 kilometers per hour. We call right to meet A per second is 29. I'm sorry. 26.39%. And the speed for speeder is 1 35 kilometers per hour. If we convert to neither perceptions 37 point by me percent. So we finally have in question. There was satisfied all this condition, which is what you find out. Square over the eye square over two ways. You could be times t plus one. Well, we finalise the final SBI off the police cough for speeding. Okay, guys, that you need to be over the police car aids the acceleration V. Here's a speed. All the speeder. He's the time they need to take to pass the speeder. And one second here is he stood because the, uh he said one second after a speeder passes that please just start axe already. So that means during his one second the speed already travel a certain distance. Okay, we just the B times one second. Okay, so we have easy question here. If we expend it will have. Um, we finally, which is B I plus 80. Okay, we find out. Is he going to indigenous being placidity? Uh, acceleration times. Time and holding square minus B I square. Okay, over two. A is equal to we t plus V. Okay. And let me put the units here. So this is one second govt times. Plus we times want sex. Okay. And he I never see. So we have We are past 82 of our square minus. We ask where and this can vehicles. Who, um, to be I plus 80 class 80 over two A is equal to we ve plus b times one second. Okay. As you can tell, you're a can take him because allow okay. And this will give us to V. I. T. Plus 80 square is equal to to a beauty. Plus to be times watch sacking. So therefore we can move everything on the left side or have 80 square plus to v i t minus two VT plus two b times. One second is equal zero. If now we're planning all these values 2.60 meters per second square times T square plus two times 26 0.3 ny meters per second ties T Linus to his eyes. There is endpoint by, you know, per second times t plus two times. Um, you know what? Every country include Boesel then. Okay, because there is no much space here, So let me do something like this. So it just minus two times 37 point by meter per second times T plus one second equals zero. Okay. And then we'll have to a point 60 media per second square times T square plus two times 26.39 You know, per second Last time, minus two times 37.5. You know, per second as time. Plus I'm sorry. Minus two times 37.5 medium per second. No times. One second is equal. Zero. This will give us 2.60 Look. Neither per second squared Times. T square. Thus 52 point 78 meters per second. Nice time. Minus 75 medium per second. That's time minus 75 meter is evil Drew. Okay. And this will give us two point 60 meter per second square times. T square is equal to, uh, sorry. Plus, actually his minus Sorry about it. So it's our minus 22 point to to meter per second times T minus certify meter is equal to zero. So I compiled combining tea turns here, which is 52 points and a meter per second minus 75 per second. And this will give us negative 22 going to through Peter per second. OK? And using this formula, we have ah, negativity plus minus square. Ooh, be square minus four a c over two A. Okay, so we need to find the ABC. Found the equation, buff. Eso eventually would have, um a t is equal to 22 0.22 you know, for a second plus and minus square. Ooh. So I into a 0.22 you know, per second holding square plus four times 75 meters. That's 2.6. You don't per second square over two times 2.6 meter per sentence. Where? Okay. And eventually, Juanito. Positive number, because the neck number doesn't make sense. Okay, because there's no negative seconds. Okay, So you have just simply, uh, it's going to 0.22 meet over second plus square ruse. Um, going to points to two meters per second and holding square plus four times. Send if I meter times 2.6 meters per second square over. Two times. 2.6 meter per seconds were okay. And this will give us the times about 11 point 14 second. Okay, So it would take about 1.14 seconds to catch the speaker. Okay? And this is the answer for the question. Thank you.


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