00:02
Here we have the graph of velocity function, and we're going to figure out when the particle is speeding up and when it's slowing down.
00:10
So what we need to know is that a particle is speeding up when the velocity and the acceleration have the same sign.
00:20
So that means they could be both positive or both negative.
00:24
And the particle is slowing down when the velocity and the acceleration have different signs.
00:33
So one positive, one negative.
00:35
So let's take a look at the graph, and let's break it down into the changing, intervals.
00:41
So it looks like it's doing something on the interval from 0 to 1, and then it's doing something different on the interval from 1 to 2, and then it's doing something different on the interval from 2 to 3.
00:54
So let's analyze the velocity and the acceleration on each of those intervals.
01:01
Okay, so when the graph is above the x -axis, the velocity is positive.
01:07
So we see that for the first interval, the velocity is positive, and for the second interval, the velocity positive.
01:13
When the graph is below the x -axis, the velocity is negative.
01:17
So from 2 to 3, the velocity is negative.
01:20
When the velocity graph is increasing, the acceleration is positive.
01:25
So we can see the velocity graph increasing from 0 to 1.
01:28
And when the velocity graph is decreasing, the acceleration is negative.
01:32
So we can see that happening from 1 to 2 and from 2 to 3...