a-cyclist-goes-downhill-for-15-min-with-a-velocity-to-ling-v4064-ttext-in-mathrmkm-mathrmh-and-then-

Question

A cyclist goes downhill for 15 min with a velocity to ling $v=40+64 t(	ext { in } \mathrm{km} / \mathrm{h}),$ and then maintains the speed at the bottom for another 30 min. How far does the cyclist go in the 45 min?

Kevin Luu · Accepted Answer

Okay, so we have a cycler and their velocity is measured by the equation V of t equals 400 minus 20 t for the interval of zero. Um, 2 10 Uh, for time. So all the questions that we have are asking us how far that they have Britain, and we can&#x27;t do that with the velocity. So we need to figure out the position equation. So the position function is found by finding the anti derivative of our distance. So assuming that&#x27;s we are starting at zero. Because we start from the first point, we can see that the function s of T is equal to 400 t minus 20. T squared over to remember that when we are finding the anti derivative of exponents, we add one to the exponents and then we divide by that number, and then plus C s of zero equals zero equals 400 time zero minus 10. I&#x27;m zero squared plus C c equals zero. So our function is going to be s of T equals 400 t minus 10 t squared. So if we do that, we can figure out all the problems. So the 1st 1 asks this How far that she they have written at five minutes. So we put s of five equals 400 times five minus 10 times five squared, which is gonna be, but it&#x27;s gonna be 2000 minus 10 times 25 which is 250. So they have would have ridden, uh, 1750 meters leaders over minutes and then before finding it at 10 minutes to do the same thing. But with 10 400 times 10 minus 10 10 squared, what gets 4000 minus 1000 that could weaken. See, that s of 10 is equal to 3000 meters. And the last question it asks us is how far the cyclists traveled when their velocity is 250 meters per minutes. So to figure that out, we&#x27;re gonna plug in 250 back into our original velocity equation. So, for a religion of velocity equation, so we have V of t equals 400 minus 20 t. We&#x27;re gonna plug in 250 into our results. We&#x27;re gonna solve this. And at 7.5 minutes were at 250 um, or travelling at 250 meters per minute. And if we want to figure out the distance, we&#x27;re gonna take 7.5 and plug it. Baggins or equation are this one. When, after some quick math, we gets 3000 minus 562.5. So we get 2000 300 are not there. 2000 437.5 meters. So you&#x27;re three answers At five minutes it&#x27;s 1750. At 10 minutes 3000. At 7.5 minutes, it&#x27;s 2437.5 meters.

Jonathon Brumley · Answer

were given a velocity function, and we want to answer some things about the distance that it travels the integral of velocity. Actually, the integral the absolute value of the velocity will tell you distance travel. But here, since the velocity is always positive, we don&#x27;t have to worry about the absolute value. The position function is the integral of the velocity function. So we&#x27;re looking at the end a girl of 400 minus 20 T, which is 400 T minus 10 t squared, plus a constant. Now we could call that constant anything we want to, uh it really doesn&#x27;t matter because it ends up canceling out. If the object started 10 meters at one position at the very beginning and and goes into the 110 the distance travelled 100. So we basically just end up subtracting the starting position away. So if I had to say the position turning positions zero, that would be the CIA&#x27;s hero. So I&#x27;m just going to say that we&#x27;ll call the initial position zero in the first part of the problem, we want to know how far the bike travels in five minutes, which is really just position at five minus position zero by filling five. That&#x27;s 2000 minus 250. And remember, the starting position was a zero position. So 2000 minus 2 50 minus zero gives us the distance Travelled of 1750 meters. Second part, we want to know how far it travels in 10 minutes, which would be s of 10 minus s of zero going into our function, that&#x27;s 4000 minus 10 times 10 square. That&#x27;s 1000 again S of 00 So that&#x27;s three 1000 meters. The last part asked us to figure out how far it&#x27;s traveled when the cyclists reaches a speed of 250 meters per minute. So the first thing we need to do is to figure out how long it takes the bike to reach a velocity of 250 meters per minute. So it set the velocity function equal to 250. Subtract the 400. It would give us negative 20 t equals negative 1 50 And if we divide by the negative 20 that 7.5. So it takes 7.5 minutes to reach that speed. Now let&#x27;s figure the position at 7.5 minutes minus position and zero five fill in 7.5 into the position equation for T. I get 3000 minus 562.5 s 00 3000 minus 5 62.5 is 2437.5 meters.

Averell Hause · Answer

So here. Let&#x27;s first convert the, um, the velocities we have Ah, initial velocity of 15 kilometers per hour. We can, uh, use a conversion one meter per second for every 3.6 kilometers per hour. And this is equaling 4.17 meters per second for philosophy final. This is 75 kilometers per hour again multiplied by one meter per second, divided by 3.6 kilometers per hour. And this is giving us 20.83 meters per second. At this point, we know that the Delta X would be four kilometers or we can simply say 4000 meters. Okay, Excuse me. So we can save the final squared equals V initial squared, plus two times acceleration times out to X. And essentially, we&#x27;re just gonna be solving for the acceleration. So the acceleration would be the final squared minus the initial squared, divided by two times Delta X b consult 20.83 meters per second squared minus 4.17 meters per second. Quantity squared, all divided by two times 4000 meters. And we find that the acceleration here is gonna be equal. Two fought. We could say a point zero 52 meters per second squared. This would be our final answer. That is the end of the solution. Thank you for watching.

Manish Kumar ( Iit K ) · Answer

So basically at least cider kilometer east for 20 minutes and then tolls head to west. Uh, two minutes for 3.2 kilometer and then 16 kilometer two is again uh, for 40 minutes. What is the higher displacement of success? So basically, if you choose starting point is our origin the origin of this one. So that means if this is a starting from over here that it east, this is west, north and south. So initially it is going for he&#x27;s going for a km east. So that means eight km And then the back with 3 3.2 km head West. So three, 3.2 km in the back with the 3.2 km. So 3.2. So that means What will be the final, this will be there. Like from here to here, that will be nothing. But it was 3.2. So that will go for mm my four point right now they again move forward of 60 kilometers right 16 kilometers. So like over here to here, 16 kilometres. Okay, so what was the total displacement? Social displacement? That will be nothing. But This 4.18 plus 16 that means 20.8 hero with right next point we need to find every since we need not intelligible city, not speed. So uh, below city, that will be nothing but could re displacement upon current time. That would total displacement is just 20.8 kilometers. So in 2000 m upon time, how much time they&#x27;re taking? Uh, in Syria, 20 minutes plus eight minutes plus 40 minutes statements total time Each 20 Plus eight plus 40. So 20 plus eight plus 40. So this would be like 60 plus 60 or eight minute minutes. So basically this velocity v in fact comes out to be 20.8. Mhm. 20.8 into 1000 Of all 16, for converting into second. So that everything we will get an assignment, right? So that means this will be like uh like this will be like 10. Get concerned, 10. So this will be like 20, Right upon 6, 8 into six. Right? So 6 8 In 26, this will be 44, So now we need to divide two 00 is still headed by 40. So it would be like In the CDDP that comes out to be 5.19. It was again, Thank you.

Emily Reynolds · Answer

in this question. We are analyzing data given to us for advice, Cliff. So it tells us that the initial velocity is 18 kilometers per hour. Now we need to convert that. So one kilometer is 1000 meters. One hour is 3600 seconds. So the initial velocity in meters per second is five meters per second. Then it also tells us that the person is final. Velocity is 75 kilometers per hour again converting one hour 300. We find that their final velocity is 20.83 meters per second. And it also tells us that the distance that the person is accelerating over is four kilometers, which is 4000 meters, and then it wants us to figure out the acceleration. Okay, so the formula that I&#x27;m gonna use is the F squared equals V. I squared plus two a Delta X. So we have 20.83 squared is equal to five squared plus two a times for 1000 her. And then when we solved through, we find that the acceleration of this person hears 0.0 five meters per second squared

Problem

A car crosses an intersection as a fire engine ap…

Problem 8 Easy Difficulty

A cyclist goes downhill for 15 min with a velocity to ling $v=40+64 t(\text { in } \mathrm{km} / \mathrm{h}),$ and then maintains the speed at the bottom for another 30 min. How far does the cyclist go in the 45 min?

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

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