00:01
Determine the position, velocity, and acceleration at t is equal to three seconds.
00:06
So the position at x is equal to three seconds, we plug in 15, 3 squared minus 5 times 3 cubed to find our position.
00:16
So let's plug that into a calculator.
00:19
We have 15 times 3 squared minus 5 times 3 cubed, and that gives us 0.
00:32
So our position is just equal to zero.
00:34
Now our velocity, v of t, is just our derivative.
00:41
So we want to, we have 30 times t minus 15 t squared, and then we plug in t is equal to three.
00:49
So we plug in 30 times three minus 15, three squared to solve for our velocity.
00:57
So 30 times three minus 15 times three.
01:04
Squared, that's equal to 765 meters per second.
01:09
So that's our velocity.
01:11
And now our acceleration is our v prime of t, which is just equal to 30 minus 30 t.
01:19
So plugging in, t is equal to 3, we have 30 minus 30 times 3, which is equal to negative 60 meters per second squared.
01:34
Now our part d also asks us to find what's the maximum positive coordinate reached up by the particle? the maximum positive coordinate is when v...