159. The following graph shows the position y = s(t) of an...

159. The following graph shows the position $y = s(t)$ of an object moving along a straight line. 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 1 2 3 4 5 6 7 8 9 10x a. Use the graph of the position function to determine the time intervals when the velocity is positive, negative, or zero. b. Sketch the graph of the velocity function. c. Use the graph of the velocity function to determine the time intervals when the acceleration is positive, negative, or zero. d. Determine the time intervals when the object is speeding up or slowing down.

Transcript

00:01 Where the velocity is positive, negative, or zero.

00:05 And so that's basically where the graph is increasing, decreasing, or constant.

00:09 So we're looking at this interval here where the velocity is increasing here and here.

00:16 Because that would be the, for what it looks like on the graph, 0 to 1 .5, and then 6 to 7.

00:26 Decreasing would be here and here, because that would be easy.

00:31 From 1 .5 to 2 and it looked like from 5 to 6 and then constant would be here and that's where our velocity would be 0 because we're in the same place so we're looking at from 2 to 5.

00:49 First see where is that to get a graph of our velocity function so let's think about this for a minute where is my velocity going to be 0 what's going to be 0.

01:02 What's going to be 0? first see where we go from increasing to decreasing or decreasing to increasing, our velocity at some point has to be zero.

01:12 So that's going to be at these points here.

01:15 So it be here and here our velocity is going to be zero.

01:18 And then also where we have this constant, that's where my velocity is going to be zero as well.

01:24 So that's going to be zero.

01:26 So what about in between there? when my velocity is increasing, then that means it's going to be above the y -axis.

01:35 So that means we're going to be having on increasing above the y -axis.

01:40 So here we're at zero.

01:41 So it's going to be increasing somewhere like here.

01:44 And then decreasing.

01:45 It's below the y -axis.

01:48 And then here we would have above the y -axis.

01:51 And we don't really know what's happening here at 7.

01:54 We just know that it's increasing...

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