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Voiceover] Johanna jogs along a straight path. And when we look at it over here, they don't give us v of 16, but they give us v of 12. And so, these are just sample points from her velocity function. So, we could write this as meters per minute squared, per minute, meters per minute squared. Fill & Sign Online, Print, Email, Fax, or Download.
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 lyrics. So, she switched directions. 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. For good measure, it's good to put the units there. For 0 t 40, Johanna's velocity is given by.
Well, just remind ourselves, this is the rate of change of v with respect to time when time is equal to 16. And so, then this would be 200 and 100. So, v prime of 16 is going to be approximately the slope is going to be approximately the slope of this line. And then, that would be 30.
So, the units are gonna be meters per minute per minute. We see that right over there. So, let's figure out our rate of change between 12, t equals 12, and t equals 20. Well, let's just try to graph. And so, these obviously aren't at the same scale. And so, this is going to be equal to v of 20 is 240. Let's graph these points here. If we put 40 here, and then if we put 20 in-between. So, at 40, it's positive 150. Johanna jogs along a straight path of exile. 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®︎/College Calculus AB. 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. And then our change in time is going to be 20 minus 12. And then, finally, when time is 40, her velocity is 150, positive 150.
We see right there is 200. So, we can estimate it, and that's the key word here, estimate. It would look something like that.