00:01
For number six, we're given these equations for the position of a particle with respect to time.
00:09
And we're asked to find the position and the speed at one sec, at zero seconds and at four seconds.
00:19
So i'm going to go through and find positions first.
00:21
So when time is zero, my x, well, you tell that's going to be zero, that's going to be zero.
00:29
They're going to add together and be zero.
00:32
And my y, same thing, that's zero, that's going to be zero.
00:36
So my position will be zero.
00:43
When t is four seconds, i'm just going to put a four in for this t.
00:53
So one half, four to the third minus two times four squared.
01:03
And that is also zero.
01:08
It's 32 minus 32.
01:09
And over here, one half four squared minus two times four.
01:20
Well, that's also zero because that's eight minus eight.
01:24
So my position for this is also zero.
01:28
And then for speed, speed is the second derivative of position.
01:36
So i'm going to find the derivative of those with respect to time.
01:42
So remember that works three times a half.
01:47
And then just raised at the second power.
01:50
Here the two comes down.
01:54
If we're here for the derivative y, that'll be two times a half, or just t.
02:04
And then that comes down, minus two.
02:10
So now the same thing...