00:01
Our goal is to find the distance and displacement of sine of t and then cosine of t on certain intervals.
00:09
And so to find the displacement, we'll start off by integrating sign, and that will end up getting us, in other words, the position function.
00:19
But of course, we're going to use the bounds here from zero up to pi halves.
00:27
And so this will actually tell us the displacement of the particle after it's, travel from 0 to pi haths.
00:34
And so the integral is going to be negative cosine of t.
00:39
But then we could just go ahead and substitute our upper limit minus subtract our lower limit, which is a minus minus.
00:50
So that turns into a plus cosine of zero.
00:59
Okay.
01:00
Cosine of pi halves is zero, cosine of one.
01:05
Sorry, cosine of zero is one.
01:08
In other words, the displacement is one at the end of this.
01:13
But because if we looked at the graph of sign here, from zero to pi halves would be all of the area under the curve here.
01:24
It's positive.
01:25
So we know that the distance that we traveled is also the same as the displacement.
01:31
If they kind of cancel each other, some of it's negative, some of it's positive, then we need to take the absolute value of everything, but we don't need to worry about that for part one.
01:40
For part two, same idea...