Johanna Jogs Along A Straight Path

We could say, alright, well, we can approximate with the function might do by roughly drawing a line here. 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 you draw a line there, and you say, alright, well, v of 16, or v prime of 16, I should say. So, the units are gonna be meters per minute per minute. They give us v of 20. Johanna jogs along a straight pathologies. And so, then this would be 200 and 100. So, at 40, it's positive 150. AP CALCULUS AB/CALCULUS BC 2015 SCORING GUIDELINES Question 3 t (minutes) v(t)(meters per minute)0122024400200240220150Johanna jogs along a straight path. But what we could do is, and this is essentially what we did in this problem. So, 24 is gonna be roughly over here. 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? Let me do a little bit to the right.

1. Johanna jogs along a straight path
2. Johanna jogs along a straight path summary
3. Johanna jogs along a straight patch 1
4. Johanna jogs along a straight path of exile
5. Johanna jogs along a straight path crossword
6. Johanna jogs along a straight pathologies

Johanna Jogs Along A Straight Path

Use the data in the table to estimate the value of not v of 16 but v prime of 16. And so, these are just sample points from her velocity function. Voiceover] Johanna jogs along a straight path. AP®︎/College Calculus AB. And when we look at it over here, they don't give us v of 16, but they give us v of 12. Johanna jogs along a straight path crossword. And so, this is going to be 40 over eight, which is equal to five. Well, let's just try to graph. We see right there is 200.

Johanna Jogs Along A Straight Path Summary

Let me give myself some space to do it. 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. So, that's that point. And so, this is going to be equal to v of 20 is 240. But this is going to be zero.

Johanna Jogs Along A Straight Patch 1

And then, finally, when time is 40, her velocity is 150, positive 150. For good measure, it's good to put the units there. Estimating acceleration. It would look something like that. Johanna jogs along a straight path summary. 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 Path Of Exile

We can estimate v prime of 16 by thinking about what is our change in velocity over our change in time around 16. It goes as high as 240. So, our change in velocity, that's going to be v of 20, minus v of 12. And so, these obviously aren't at the same scale.

Johanna Jogs Along A Straight Path Crossword

And then, when our time is 24, our velocity is -220. When our time is 20, our velocity is going to be 240. We see that right over there. If we put 40 here, and then if we put 20 in-between. 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. 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. This is how fast the velocity is changing with respect to time. For 0 t 40, Johanna's velocity is given by. 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. So, -220 might be right over there.

Johanna Jogs Along A Straight Pathologies

They give us when time is 12, our velocity is 200. And then our change in time is going to be 20 minus 12. And we see on the t axis, our highest value is 40. 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, they give us, I'll do these in orange. Let's graph these points here. And then, that would be 30. So, when our time is 20, our velocity is 240, which is gonna be right over there.