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And so, then this would be 200 and 100. So, -220 might be right over there. They give us when time is 12, our velocity is 200. AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES Question 3 t (minutes) v(t)(meters per minute)0122024400200240220150Johanna jogs along a straight path.
Johanna Jogs Along A Straight Path Meaning
Well, just remind ourselves, this is the rate of change of v with respect to time when time is equal to 16. 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? Johanna jogs along a straight path. It goes as high as 240. We go between zero and 40. And we see here, they don't even give us v of 16, so how do we think about v prime of 16. We see right there is 200.
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If we put 40 here, and then if we put 20 in-between. So, 24 is gonna be roughly over here. When our time is 20, our velocity is going to be 240. Johanna jogs along a straight pathé. 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. So, the units are gonna be meters per minute per minute. Well, let's just try to graph. So, she switched directions.
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But what we could do is, and this is essentially what we did in this problem. So, when the time is 12, which is right over there, our velocity is going to be 200. So, when our time is 20, our velocity is 240, which is gonna be right over there. And so, this would be 10. We can estimate v prime of 16 by thinking about what is our change in velocity over our change in time around 16. AP®︎/College Calculus AB. For 0 t 40, Johanna's velocity is given by. So, our change in velocity, that's going to be v of 20, minus v of 12. Johanna jogs along a straight path meaning. 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. So, that is right over there.
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For good measure, it's good to put the units there. 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, when our time is 24, our velocity is -220. Let me give myself some space to do it. 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. So, if we were, if we tried to graph it, so I'll just do a very rough graph here. And so, these are just sample points from her velocity function. And then our change in time is going to be 20 minus 12. And we don't know much about, we don't know what v of 16 is.
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We could say, alright, well, we can approximate with the function might do by roughly drawing a line here. 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 40 over eight, which is equal to five. So, at 40, it's positive 150. So, that's that point. Let me do a little bit to the right. Fill & Sign Online, Print, Email, Fax, or Download. And so, these obviously aren't at the same scale. But this is going to be zero.
And we would be done. So, they give us, I'll do these in orange. So, this is our rate.