00:01
Okay, so there's a constant acceleration of 6 feet per second squared, but there's deceleration of v squared over 600.
00:11
So that means the acceleration is 6 minus v squared over 600.
00:21
You want to find the velocity.
00:25
So acceleration is equal to the derivative of the velocity with respect to time.
00:35
Another way to write this is 3 ,600 minus v squared over 600.
00:47
So dv is equal to 3 ,600 minus v squared over 600 d t.
00:58
And then we are going to integrate both sides.
01:09
Oh, excuse me, we need to flip it.
01:12
So it is 600 over 3 ,600 minus v squared dv.
01:37
V.
01:37
We'll put the 600 on the other side.
01:41
This is dt over 600.
01:49
Then you're going to take the integral of both sides.
01:57
This is the same as 1 over 6 .000.
02:05
6 squared minus v squared dv is equal to d t over 600.
02:15
So this is 1 over 2 times 60 ln of 60 plus v over 60 minus v and this is t over 600.
02:33
We're going to put the plus c on this side.
02:36
So it says it's initially at rest, so the initial velocity is zero.
02:47
Since the initial velocity is zero, that's one over.
02:53
That means the constant is zero.
02:55
If the initial velocity is zero, the constant is zero...