00:02
All right, looks like you tried to cut and paste a large number of multiple choice questions all in one question, which i really made it difficult to read what was happening.
00:16
So i'm not able to complete all of the questions for you.
00:21
Plus, we shouldn't be adding so many in one because it's difficult for us to answer all of them without taking over an hour to do.
00:33
Next time, try to cut and paste one or two multiple choice at once, and we can solve those without having to try to guess what all of them were, because i can't figure out a handful of them there.
00:49
So number one is an example.
00:51
I can't figure out what it's actually asking.
00:54
I know that it has to do with that you're trying to figure out what the acceleration time function is.
01:01
So i'm going to, in general terms, how do you find the acceleration time function when i know the position time function or the velocity time function? because that's questions one and two.
01:17
The double derivative of the position time function is acceleration.
01:22
That's the definition of acceleration.
01:24
So if i had a, i'm just going to make up one here because i couldn't really make out what the equation was.
01:32
It didn't translate over very well.
01:34
So let's say that i have an x over t function that's 4x to the third plus 3x.
01:44
If i want to take the derivative of that, i get 12x squared plus 3.
01:57
Well, that is equal to the velocity time function.
02:02
The single derivative of the position time is the velocity time function.
02:07
Now, if i take the derivative again, that is going to get me the acceleration time function.
02:13
So the double derivative here is going to be 24x.
02:21
So that's how we can find the acceleration when we know the position time function.
02:27
Now that we have the function, you just plug in whatever number you need.
02:31
So if it was at three seconds, what's the acceleration at three seconds, three times 24? what's the position at three seconds? four times three to the third plus three times three, whatever that is, that will tell you the displacement of it.
02:48
What's the velocity at that time? that's 12 times three squared plus three.
02:53
That'll tell you how fast it was going at three seconds.
02:55
So the nice thing about the derivatives is we can now predict all three of these aspects of motion simultaneously if we have the position function.
03:06
So number two is very similar, but that's the derivative of the velocity function.
03:14
I'll tell you the acceleration, and i kind of set that up as an example.
03:21
Number three, again, it's a calculus -based question about what's happening if my function is 54 plus 2t to the third power.
03:32
It's definitely still has an acceleration because the factor, if i do the derivative, i still have a 12t.
03:41
For the acceleration function.
03:44
So no matter what time, we're still, we still have an acceleration, and it's a varying acceleration.
03:51
So there's no rest happening here, and there's definitely some acceleration, and it's continuing to move, even though at one point it might be at zero...