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An object starts from rest and undergoes uniform acceleration. From 1.078 to 10.698 it travels 4.6m. What is the average velocity of the object during the time inte...

Question

An object starts from rest and undergoes uniform acceleration. From 1.078 to 10.698 it travels 4.6m. What is the average velocity of the object during the time interval 18.948 to 26.77s (in ")?

An object starts from rest and undergoes uniform acceleration. From 1.078 to 10.698 it travels 4.6m. What is the average velocity of the object during the time interval 18.948 to 26.77s (in ")?



Answers

An object initially at rest experiences an acceleration of $1.5 \mathrm{~m} / \mathrm{s}^{2}$ for $6.0 \mathrm{~s}$ and then travels at that constant velocity for another $8.0 \mathrm{~s}$. What is the object's average velocity over the 14 -s interval?

Yeah, we want to find the magnitude of the average velocity of an object. If that object moves from the position D one equals 2.0 m. Made. A 3.0 m to position D 25.0 m, making a 9.0 m and T equals 2.4 seconds. This question is challenging our fundamental understanding of velocity and of basic cinematics. So the magnitude of the average velocity here, it's just going to be equal to the change of distance over the change in time in the given time period. We can calculate for the change in distance or delta D. Using the distance formula and our two given points. Do you want to do to the delta P equals square root of X two minus x one squared plus 20 minutes. Why one squared or square root of five minutes? Two squared plus 99 plus three squared. This is just three squared plus negative square square rooted or 6.7 m were given delta T equals 2.4 seconds, so then the average is going to be 6.7 m over 2.4 seconds, or an average velocity magnitude of 2.8 m per second.

All right, So we're looking at the velocity function T squared plus three t from 0 to 6. So the average velocity, it's going to be just the same formula as the average value. And, uh so from 0 to 6 that's gonna reduce the 16 So are in a rule is gonna be t cubed at add one to your exponents and then divide by it. So three has because we had to add one to our exponents and divide by it and thats from 0 to 6. So as we again, they choose zero for a reason. Cause plugging in zero here you're going to get a bunch of zeros are looking at 16 times 1/3 time six cubed plus three has time six squared again If you've been following a long I have short cuts in here because when you distribute this 16 in here, it boils down to 1/3 time. Six. Squared because you can cancel on those sixes and same thing with this 13 have times six. We can cancel out one of them when you distribute in. So six words 36 36. Divided by three 12 six centuries. 18 divided by two is nine and the average velocity on this intervals 21

So here we need to calculate the distance traveled during the excellence. The distance can be returned as questions as This will be equals two. U. T. Less of it is square. Let us substitute the values so you're given you has given us four and time he's equals two fives and plus. Uh huh Multiplied by the acceleration is given as 1.2 m person and square Well played. Where time has given us five seconds. After calculation, we will get the required distance table in the given time. And trouble is Comes out to be 35. Make this so this is the required distance table then we have in Israel Spirit It's a little bit you is equals two four metre purse again And time is equals two. What was the game acceleration during this time? And trouble is it close to 1.2 Metre position is So this we have got us 35 m

So here we have a lot of givens that we have Tio convert. We have velocity ex initial velocity. Why initial velocity X final and velocity. Why final? This is going to equal velocity exponentially, Kal. 625 kilometers per hour. We're going to have to convert two meters per second so 1,000 meters per every kilometre and then for every hour we have 36 hundreds seconds and so this is giving us 173.6 meters per second. Now for the other ones, we can simply say 415 times 1,000 divided by 36 100 and this is giving us 115.3 meters per second. And we know that the initial equals 3.85 seconds of the X final. We know to be 838 kilometres per hour or we can say 38 times 1,000 divided by 36 100 and we're getting 232.8 meters per second. And then finally we have 365 kilometers per hour times 1,000 divided by 36 100. You're just doing the same exact conventions over and over again. And then this equals 101.4 meters per second and you know that T final equals 6.52 seconds. So the question is asking us to ah, essentially calculate acceleration The X and Y components, the magnitude of the acceleration and the direction So we can say that the white component is simply going to be v Y Final money's the Y initial. So we'll have 100 1.4, minus 115.3 and then divided by T final modesty National So 6.52 minus 3.85 and we're getting this is equal to negative 5.206 meters per second squared now the ex component of velocity should be the V X final matters VX initial, of course, divided by the change in time so to 32.8 minus 173.6, divided by 6.52 minus 3.85 And this is giving us 22.172 meters per second squared s o. We can say that the magnitude of the acceleration is simply going to be the square root of the sum of the squares. This will be negative. 5.206 squared plus 22.172 squared to the 1/2 power and this is giving us 2.97 meters per second squared. So this would be our magnitude of the acceleration vector. And then to find the angle, you simply take arc Tan of the Why component divided by the ex component. So 22 0.172 Rather, that's the ex component. My apologies. It would be a negative 5.206 The y component of velocity divided by the ex component 22.172 and we're getting that data equals 30 13.2 degrees. And again, your ex is positive. But your why is negative. So this is going to be below positive ex access. So this would be your direction. That is the end of the solution. Thank you for watching


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