They give us v of 20. Let's graph these points here. So, when the time is 12, which is right over there, our velocity is going to be 200. We go between zero and 40. So, if you draw a line there, and you say, alright, well, v of 16, or v prime of 16, I should say. Johanna jogs along a straight paths. And then, that would be 30. So, they give us, I'll do these in orange. Voiceover] Johanna jogs along a straight path. And so, let's just make, let's make this, let's make that 200 and, let's make that 300.
So, if we were, if we tried to graph it, so I'll just do a very rough graph here. AP®︎/College Calculus AB. So, let me give, so I want to draw the horizontal axis some place around here. Johanna jogs along a straight path wow. So, 24 is gonna be roughly over here. And so, then this would be 200 and 100. And then, finally, when time is 40, her velocity is 150, positive 150. That's going to be our best job based on the data that they have given us of estimating the value of v prime of 16. AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES Question 3 t (minutes) v(t)(meters per minute)0122024400200240220150Johanna jogs along a straight path. It would look something like that.
So, that's that point. Let me give myself some space to do it. Use the data in the table to estimate the value of not v of 16 but v prime of 16. Let me do a little bit to the right. 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. And we see on the t axis, our highest value is 40.
Fill & Sign Online, Print, Email, Fax, or Download. This is how fast the velocity is changing with respect to time. 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. So, she switched directions.
They give us when time is 12, our velocity is 200. So, we can estimate it, and that's the key word here, estimate. So, v prime of 16 is going to be approximately the slope is going to be approximately the slope of this line. It goes as high as 240. And so, what points do they give us? So, -220 might be right over there. And we see here, they don't even give us v of 16, so how do we think about v prime of 16. When our time is 20, our velocity is going to be 240.
If we put 40 here, and then if we put 20 in-between. And so, this is going to be equal to v of 20 is 240. And we would be done. And then our change in time is going to be 20 minus 12.
So, this is our rate. But what we could do is, and this is essentially what we did in this problem. Estimating acceleration. So, our change in velocity, that's going to be v of 20, minus v of 12. So, let's say this is y is equal to v of t. And we see that v of t goes as low as -220. But this is going to be zero. For good measure, it's good to put the units there.
So, the units are gonna be meters per minute per minute. And when we look at it over here, they don't give us v of 16, but they give us v of 12. 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 so, this would be 10.
So, we could write this as meters per minute squared, per minute, meters per minute squared.
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