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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. We could say, alright, well, we can approximate with the function might do by roughly drawing a line here. So, that is right over there. So, at 40, it's positive 150. And when we look at it over here, they don't give us v of 16, but they give us v of 12. Use the data in the table to estimate the value of not v of 16 but v prime of 16. So, our change in velocity, that's going to be v of 20, minus v of 12. Voiceover] Johanna jogs along a straight path. AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES Question 3 t (minutes) v(t)(meters per minute)0122024400200240220150Johanna jogs along a straight path. They give us when time is 12, our velocity is 200. So, that's that point. So, -220 might be right over there. Johanna jogs along a straight path pdf. Let's graph these points here.

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Johanna Jogs Along A Straight Path

And then our change in time is going to be 20 minus 12. They give us v of 20. Let me do a little bit to the right. And so, let's just make, let's make this, let's make that 200 and, let's make that 300. For 0 t 40, Johanna's velocity is given by. This is how fast the velocity is changing with respect to time.

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Fill & Sign Online, Print, Email, Fax, or Download. So, the units are gonna be meters per minute per minute. So, 24 is gonna be roughly over here. And so, these are just sample points from her velocity function. Johanna jogs along a straight path lyrics. So, if we were, if we tried to graph it, so I'll just do a very rough graph here. If we put 40 here, and then if we put 20 in-between. It would look something like that. Well, let's just try to graph. So, they give us, I'll do these in orange.

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So, if you draw a line there, and you say, alright, well, v of 16, or v prime of 16, I should say. We can estimate v prime of 16 by thinking about what is our change in velocity over our change in time around 16. 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. So, she switched directions. We see right there is 200.

Johanna Jogs Along A Straight Path. For 0

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 so, these obviously aren't at the same scale. And so, then this would be 200 and 100. So, this is our rate.

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And we don't know much about, we don't know what v of 16 is. Well, just remind ourselves, this is the rate of change of v with respect to time when time is equal to 16. 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. When our time is 20, our velocity is going to be 240. For good measure, it's good to put the units there. And so, this is going to be 40 over eight, which is equal to five. And we see here, they don't even give us v of 16, so how do we think about v prime of 16. Johanna jogs along a straight path. So, when our time is 20, our velocity is 240, which is gonna be right over there. We go between zero and 40. So, we can estimate it, and that's the key word here, estimate.

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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, let me give, so I want to draw the horizontal axis some place around here. It goes as high as 240. But this is going to be zero. And we would be done. So, when the time is 12, which is right over there, our velocity is going to be 200. Estimating acceleration. And so, what points do they give us? So, we could write this as meters per minute squared, per minute, meters per minute squared. AP®︎/College Calculus AB. We see that right over there. And then, that would be 30. So, let's figure out our rate of change between 12, t equals 12, and t equals 20. And so, this is going to be equal to v of 20 is 240.

And so, this would be 10. But what we could do is, and this is essentially what we did in this problem. So, v prime of 16 is going to be approximately the slope is going to be approximately the slope of this line.

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