So, at 40, it's 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. 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 then our change in time is going to be 20 minus 12. Voiceover] Johanna jogs along a straight path. Johanna jogs along a straight paths. 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, this is our rate. So, they give us, I'll do these in orange. 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. AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES Question 3 t (minutes) v(t)(meters per minute)0122024400200240220150Johanna jogs along a straight path. So, when the time is 12, which is right over there, our velocity is going to be 200.
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Johanna Jogs Along A Straight Path Youtube
So, we can estimate it, and that's the key word here, estimate. And so, this would be 10. We go between zero and 40.
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And so, this is going to be 40 over eight, which is equal to five. And then, finally, when time is 40, her velocity is 150, positive 150. Let's graph these points here. Well, just remind ourselves, this is the rate of change of v with respect to time when time is equal to 16.
Johanna Jogs Along A Straight Pathfinder
And so, these are just sample points from her velocity function. But this is going to be zero. And when we look at it over here, they don't give us v of 16, but they give us v of 12. So, let's figure out our rate of change between 12, t equals 12, and t equals 20. When our time is 20, our velocity is going to be 240. But what we could do is, and this is essentially what we did in this problem. 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? So, 24 is gonna be roughly over here. AP®︎/College Calculus AB. Johanna jogs along a straight pathfinder. For good measure, it's good to put the units there.
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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. It goes as high as 240. We can estimate v prime of 16 by thinking about what is our change in velocity over our change in time around 16. 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. Johanna jogs along a straight pathé. And so, these obviously aren't at the same scale. So, -220 might be right over there. It would look something like that.
Johanna Jogs Along A Straight Pathé
And we don't know much about, we don't know what v of 16 is. This is how fast the velocity is changing with respect to time. We see right there is 200. And then, that would be 30. So, let me give, so I want to draw the horizontal axis some place around here. We see that right over there. If we put 40 here, and then if we put 20 in-between. So, if you draw a line there, and you say, alright, well, v of 16, or v prime of 16, I should say. And so, this is going to be equal to v of 20 is 240.
So, when our time is 20, our velocity is 240, which is gonna be right over there.
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