00:01
Here, we're given the equation for the position of a particle.
00:05
And we want to find its velocity and acceleration.
00:08
So the velocity will just be the derivative of the position.
00:12
So we have the power rule.
00:14
Take the three out front and you have a squared minus three, because the derivative of 3t is just 3.
00:21
Now that we have the velocity, let's go ahead and find the acceleration, which is its derivative.
00:26
So we have t squared, the 2 comes out front, so 2 times 3 is 6, and then we have a t since 2 minus 1 is 1.
00:33
And then minus, well, the three goes away.
00:35
So it's just 6t.
00:37
Now that we know the velocity and acceleration, we can answer the rest of the questions.
00:43
Find the acceleration after four seconds.
00:45
So the acceleration at four seconds, well, that's just going to be six times four, because that's 6t, where if t is 4...