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Port_Submission519808/quizzes/2081407 /takeQuestion 65 pts2CCalculate the accelerationin feetpersecond? necessary to go from a velocity of 30 miles per hour to zero...

Question

Port_Submission519808/quizzes/2081407 /takeQuestion 65 pts2CCalculate the accelerationin feetpersecond? necessary to go from a velocity of 30 miles per hour to zero miles per hour in a distance of 1.0 inch: Hints: 30 miles per hour is 44 feet per second, 1.0 inch is 0.0834 feet: You can use eq: 2.11ofthe interactive textbook: The problem has not told you anything about time; because time is not needed to solve the problem: although acceleration from slowing down should be negative ignore the min

Port_Submission 519808/quizzes/2081407 /take Question 6 5 pts 2C Calculate the accelerationin feetpersecond? necessary to go from a velocity of 30 miles per hour to zero miles per hour in a distance of 1.0 inch: Hints: 30 miles per hour is 44 feet per second, 1.0 inch is 0.0834 feet: You can use eq: 2.11ofthe interactive textbook: The problem has not told you anything about time; because time is not needed to solve the problem: although acceleration from slowing down should be negative ignore the minus sign when giving the answer The correct answer is = positive number:



Answers

A car starts moving at time $t=0$ and goes faster and faster. Its velocity is shown in the following table. Estimate how far the car travels during the 12 seconds. $$\begin{array}{c|c|c|c|c|c} \hline t \text { (seconds) } & 0 & 3 & 6 & 9 & 12 \\ \hline \text { Velocity (ft/sec) } & 0 & 10 & 25 & 45 & 75 \\ \hline \end{array}$$

So here for this problem we are going to be specifically looking at a table of values and using the table values to find average acceleration that's going to be given to us as the velocity T plus H minus, lost the at T. All divided by H where H does not equal zero. But since we know our cable values, we want to find our initial average acceleration. So it's gonna be when t. equals zero um and H is equal to one. So that's going to end up giving us 30 as a result. And then we want to find the average acceleration for the 2nd, 2nd says can be V. Of one plus one. Um So now we have that T. Equals one and H equals one. And when we do that we end up getting our answer to be 22.

Told that a cars accelerating from 0 to 60 MPH and 30 seconds at a constant acceleration. And so how fast the cars traveling after this 30 seconds is just going to be equal to this 60 MPH, Since we're told that we accelerate up to 60 MPH to constant acceleration and then we're just going to be going 60 MPH After that. So this is equal to 60 mph. And then for part B we're going to figure out Um the distance traveled in the 1st 30 seconds. So the first thing that we're gonna want to do to figure this out is convert the 60 mph, two mph. So you have 60 mph. We're going to multiply by one hour per 60 minutes And then we're going to multiply it by one minute Per 60 seconds. So now these units will cancel, these units will cancel and we'll be left with miles per second. So this is going to be equal to 1/60 and this is in miles per second. And then what we can do to actually figure out the acceleration is we're going to just multiply by 1/30 seconds since we're told that we're accelerating at a constant acceleration. That means that in every second in the 1st 30 seconds we have the same acceleration so we can just divide by 30 seconds to get our acceleration in miles per second. So this is equal to one over 900, I'm sorry, This is equal to one over 1800 and this is in miles per second. And now we can actually find the distance traveled. So and this is per second squared actually. So now we have this constant acceleration, we can find the integral of our constant acceleration and I'm gonna say D. T. And this will be equal to our velocity equation. So this is equal to T over 180. And now we're 1800. And now we can do is we can find the integral of this Um from 0 to 30 to find the distance traveled in the 1st 30 seconds and it will be given in miles. So the integral of tea over 1800 From 0 to 30, it's equal to t squared over 30. 600. And I just Added 1 to the exponent and then divided by whatever that exploded is in this case it is too and this is from 0 to 30 and we don't have to worry about C since we are going from rest. So when V. Is equal to your, sorry, when our function D. F. T. Is equal to zero, we're gonna have gone zero m. So see is can be equal to zero here. So now we just have to look at when T. Is equal to zero and T is equal to 30 so in T. Is equal to zero, this is equal to zero. So now really all we have to look at is when T is equal to 30 20 is equal to 30 we get 900 Divided by 30 600, and this is in miles. And we can simplify this to being 1/4 miles. So the distance traveled in the 1st 30 seconds of this car would be 1/4 miles.

To 60 MPH. That is a culture mhm 62 1609 About 3600 Mita for 2nd, 26.8 million books. Second, the is what, 80 MPH that is 40 a into 1609 upon upon 36. 17.9 m per second end. They is three second now. First magnitude off acceleration is you might not be appointee. There is 28 26.8 minus 17.9 upon three is a girl toe 3 m per second square And second, um, the girls through 9.8 beat bar square feet per second. Now we know that we square is equal to you Square plus twice s No, The 17.9 square you is 26.8 square last twice a is three into s. So this is a girl too. 66.3 We go

Problem. 32 on V is equal to 60 MPH, which is equal to 88 ft per second. So a off T equals to a negative 11. We off t is equal to integration off the off TV T, which is, I think, 11 integration off DT to equal toe eleventy posse as we know it is equal to 88 So C is equal to 88. So we are looking toe 11 plus 18 eight negatively living teeth plus 88. So, um, when we off t people 45 my our which is 66 ft per second. So 66 is equal to a negative 11 t plus 88 so t is equal toe two seconds. So therefore the part takes two seconds until it treats the speed off 45 feet per second. For question, be x o. T. Is equal to the integration off negative eleventy plus 88 BT which is equal to negative 11 over to T square, which waas 88 DeBrosse So when t is equal to zero, X note is equal to zero, so C is equal to zero, so xrt is able to negative eleventy squared over two plus 80 80. So when the car stopped at the off, the equal to zero S O. T is equal to eight seconds S o X off t in the community, 11 over to eight squared, plus 88 times times eight, which is 22 35 2 ft. So therefore the cars traveled 352 ft before.


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