00:01
So for this problem, i feel like the question is sort of out of order t squared plus 23t because before i figure out the total distance, i would want to figure out the derivative of this, which will give me velocity.
00:25
So as i just do the power rule, i get 3t squared minus 8 times 2 of 16, subtract 1 .5.
00:33
From the exponent and then plus 23.
00:36
And i want to see where this equals zero.
00:39
So what i'm going to do is a quadratic formula just to see when the velocity equals zero.
00:45
And that'll be t equals negative b, plus or minus b squared, which when you square a negative becomes a positive anyway, minus four times three, times 23, all over 2a.
00:58
And we have an issue here is that what's under the radical, i'll switch back to red, is a negative.
01:11
So what that means is that we have imaginary roots, which means that this can never equal zero, at least not in the real sense.
01:21
So the total distance traveled, now i can actually answer part a on the, for the first six seconds.
01:30
So what i need to do is figure out what half of zero is.
01:32
We'll plug in zero and all three of those t's, you'll get zero.
01:35
But then we need to figure out what f of 6 is.
01:39
And i'm just using my calculator and plugging in 6 and for all those t's.
01:44
So 6 cubed, minus 8 times 6 squared, plus 23 times 6.
01:52
And i got 66.
01:54
So what that means is if i find the difference between those two, the total distance traveled would be 66, whatever the units were.
02:04
I think they said feet...
