Estimating acceleration. But what we wanted to do is we wanted to find in this problem, we want to say, okay, when t is equal to 16, when t is equal to 16, what is the rate of change? When our time is 20, our velocity is going to be 240. We go between zero and 40.
We see right there is 200. Let me do a little bit to the right. For zero is less than or equal to t is less than or equal to 40, Johanna's velocity is given by a differentiable function v. Selected values of v of t, where t is measured in minutes and v of t is measured in meters per minute, are given in the table above. And then our change in time is going to be 20 minus 12. And so, this is going to be equal to v of 20 is 240. Johanna jogs along a straight path crossword clue. So, if you draw a line there, and you say, alright, well, v of 16, or v prime of 16, I should say. We could say, alright, well, we can approximate with the function might do by roughly drawing a line here. So, at 40, it's positive 150. And so, this would be 10.
Let's graph these points here. So, when our time is 20, our velocity is 240, which is gonna be right over there. And then, finally, when time is 40, her velocity is 150, positive 150. They give us v of 20. It goes as high as 240. Johanna jogs along a straight path. for 0. Well, let's just try to graph. So, -220 might be right over there. For 0 t 40, Johanna's velocity is given by. This is how fast the velocity is changing with respect to time.
And we don't know much about, we don't know what v of 16 is. So, let's say this is y is equal to v of t. Johanna jogs along a straight pathé. And we see that v of t goes as low as -220. So, v prime of 16 is going to be approximately the slope is going to be approximately the slope of this line. So, we literally just did change in v, which is that one, delta v over change in t over delta t to get the slope of this line, which was our best approximation for the derivative when t is equal to 16.
And so, these obviously aren't at the same scale. We see that right over there. So, she switched directions. And then, that would be 30. And when we look at it over here, they don't give us v of 16, but they give us v of 12. And we would be done. Use the data in the table to estimate the value of not v of 16 but v prime of 16. So, that is right over there.
So, 24 is gonna be roughly over here. So, let me give, so I want to draw the horizontal axis some place around here. They give us when time is 12, our velocity is 200. So, that's that point. Well, just remind ourselves, this is the rate of change of v with respect to time when time is equal to 16.
Fill & Sign Online, Print, Email, Fax, or Download. And we see here, they don't even give us v of 16, so how do we think about v prime of 16. Now, if you want to get a little bit more of a visual understanding of this, and what I'm about to do, you would not actually have to do on the actual exam.