And so, then this would be 200 and 100. So, -220 might be right over there. And so, let's just make, let's make this, let's make that 200 and, let's make that 300. We see right there is 200. So, that's that point. So, when the time is 12, which is right over there, our velocity is going to be 200. It would look something like that.
So, when our time is 20, our velocity is 240, which is gonna be right over there. Let's graph these points here. And then our change in time is going to be 20 minus 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.
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. 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 so, these obviously aren't at the same scale. Well, let's just try to graph. And then, when our time is 24, our velocity is -220. So, 24 is gonna be roughly over 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 pathé. 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. And so, this would be 10. So, that is right over there. When our time is 20, our velocity is going to be 240.
We see that right over there. They give us when time is 12, our velocity is 200. So, we could write this as meters per minute squared, per minute, meters per minute squared. So, at 40, it's positive 150. But what we could do is, and this is essentially what we did in this problem.
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