00:01
Okay, so we're given a function x of t equals 2 t e to the minus t.
00:05
And the way to do this is to first calculate the velocity and acceleration.
00:10
The velocity and acceleration are just the derivatives of x of t.
00:14
So velocity is the first derivative and we do it through product rule.
00:18
And acceleration is the second derivative, which again, we do again by product rule.
00:24
So i'm not going to i'm not going to spend too much time on them.
00:29
But the point is that you need to find when acceleration is equal to zero.
00:33
So this is the same thing as when 4e to the minus t is equal 2 t e to the minus t.
00:38
And then you can divide out 2 and e to minus t since they're always positive, and you just get left with t equals 2.
00:46
And so the first question asks you, the first question asks you, what's the velocity at the time when acceleration equals 0? so this is just velocity at 2 is equal to this, which is this...