00:01
Okay, so we're given this velocity function.
00:02
Here's the constants that go into it.
00:05
And we wanna find the position and acceleration at two and at five.
00:11
We're told that x of one is equal to zero.
00:15
Okay, so let's start with the acceleration.
00:18
So the acceleration is dv dt.
00:23
And so the a, we just get zero and minus b over t squared will be that, okay? so a at two is minus my b, which is 0 .24 divided by four, which is minus 0 .06.
00:49
That's gonna be meters per second squared.
00:53
A of five is minus 0 .24 over 25, which comes out to be minus 9 .6 times 10 to the minus three.
01:20
That's also in meters per second squared.
01:25
And then x of two, well, first of all, x of t.
01:37
So x of t, we have to integrate the velocity.
01:40
So we get a t plus b times log of t plus some constant...