00:01
Here, we're given the equation for the velocity of a particle, and we're asked some details about how much position has changed.
00:08
So before we start off answering these questions, i'm just going to define some areas.
00:13
So first off, we have a square here, and the total distance from zero to two is going to be that area inside that.
00:21
So this is a 2 by 1, so this has a total area of 2.
00:25
Likewise, we have a triangle here.
00:28
It's 2 by 1, but it's a triangle, so it's a 1.
00:31
And then we have another triangle here.
00:34
That's one, two, three by one, so three halves is its area.
00:38
And then we can also say, well, we have a rectangle here.
00:41
And that's a two by three, so an area of six.
00:45
Now that i've calculated all that, it's a lot easier to go in and answer the questions.
00:50
How far did it travel in the first two seconds? well, in the first two seconds, that's from zero to a two.
00:56
What's the area under the curve? well, two.
01:00
For part b, the distance travel will be...