00:01
Explosion causes debris to rise vertically with a initial velocity of 112 feet per second.
00:06
The function is right here describes the height of the debris above the ground.
00:11
What is the instantaneous velocity of the debris one second after the explosion and five seconds after the explosion as well as the instantaneous velocity of the debris when it hits the ground? so for part a, we're going to just simply take the derivative of our position function.
00:27
That's going to give me a velocity.
00:28
So when i do that, i'm going to take two down here, multiply it out.
00:35
So my velocity in terms of time is equal to a negative 32t plus 112.
00:44
Because we take the derivative of 112t, it just becomes 112.
00:50
So if i look at v of 1, that's going to be negative 32 times 1 plus 112.
00:57
12.
00:59
So v of 1 is going to be negative 32 plus 112.
01:03
So that's going to give me 80.
01:05
So after one second is 80 feet per second.
01:09
If i do the same thing for v of 5, so that's negative 32 times 5 plus 112.
01:16
Okay.
01:17
So negative 32 times 5 plus 112.
01:20
And i get negative 48.
01:24
Okay...