0:00
Hi.
00:01
In this video, we're given that an object is thrown up with a velocity given by this function negative 32t plus 71, starting from a height of 38 feet.
00:14
And so we're just going to answer a few questions about this scenario.
00:17
So the first one says, what is the object's initial velocity? so that's just v of zero, which you have correctly written here already, is 71.
00:28
For b, what is the object's maximum velocity? and so for this one, we have to imagine that the, well, we see that the velocity function is a downwards line, right? so as you also correctly pointed out, the maximum is just at the beginning.
00:49
So also 71.
00:53
Now, c, what is the object's maximum displacement? so now what we need to do is come up with the displacement function, which i'll call d of t, which is the antiderivative, and then we use the fact that the initial height was 38.
01:08
So the anti -derivative is negative 16 t squared plus 71t plus the initial height.
01:17
So negative 16 t squared, i guess this should be d of 0, plus 71t plus 38.
01:28
So then the vertex of this is going to be at t equals we use negative b over 2a.
01:35
So negative 71 over 2a is negative 32...