Okay, so we have a car moving in a straight path, and we record the time and its corresponding position. And so, um, those times and corresponding positions are as follows. So we have the time in seconds and the position in feet. And so a time zero where a position zero at time to were at position 10 feet. And then time four, we're 14 6 20 eight, 30 and 10 were at 36. Okay. And so what we want to do is for the following, we want to find wth e average velocities, um, for these different time frames, and so we want from 0 to 2 seconds. Okay, so the 1st 1 is from 0 to 2 seconds, and so we know that is gonna be, um, 10 minus zero. So it's gonna be the differences of our positions divided by the difference of our time. So this is going to be five, um, feet per second. Okay. And then we want to do part B. We want to do from two to four seconds, and so we would have 14 minus 10 over, um, four minus two. So this would be two feet per second okay. And then part see, we would want to do from for two six seconds. And so 20 minus 14. Over too is three feet per second. And in part D is six to eight seconds. And so we have 30 minus 20 divided by two. Which gives me the five feet per second. Okay. And then what we want to do in E There's a couple things we want to do. An E. We want to estimate the instantaneous velocity at T equal to four seconds, and we want to do it several different ways. We want to. Actually, first way is to determine it by, um, finding the average velocity between two and six seconds. So when we find the average velocity from 2 to 6, so we want to find it from finding the average velocity, um, from two, 26 seconds. And so that is going to be 20 minus 10 divided by four seconds, which is two and 1/2 feet per second. And then what we wanted to the second time is to average my answers from part B, and I believe it waas part. Um see. And so we got, um, that would be two plus three. Divide by two, and we get 2.5 feet per second. Okay, um and then what we want to do is an f We want to do the exact same thing. We want to know the instantaneous velocity, um, at T equal to six seconds, and we want to do it the exact two ways we want to find theat bridge velocity. Um, from I believe it's gonna be from average velocity between, um too. And I've got what we did. 30 and 14 um, four and eight. And so this would be 30 minus 14. Divide by four. So this gives me four feet per second. And then what we want to dio is to, um, find it by, um, averaging my answers from and we're going to do from 4 to 6 from C and D. And so when we do that, we get, um, three plus five, divide by two. Which gives me four feet per second. Okay, Now, in G G says we notice So if you didn't notice, um, when we go back here, um, we got two and 1/2 feet per second. Two and 1/2 feet per second, and then we got four feet per second and four feet per second. So, um, whether we did it for, um, the average or we did it by averaging two separate answers. We got the exact same answers. And so the question is, Is, um well, this always be the case. Um and, um, he's kind of Ah, double edge. Um answer. Um, yes, as long as your increments or the same. Um, And what I mean by that is, if you notice here on both of these, we went from 4 to 6 and 6 to 8. Um, and so six was right exactly in the middle of foreign ate here we went from, um um we went from 2 to 4 and 4 to 6. So, um, if those incremental steps are the same, Yes. Um, but if I try to, um, let's say I wanted to know what it waas at at, um t equal to six seconds. Okay? And what I did waas I found, um first I found from to two six. Then I did six toe eight, and then I average those together. And so if I do 2 to 6, um, this would be 20 minus 10. And I have, um, four seconds here. So that gives me, um, five over to which is 2.5 feet, um, per second. And then from 6 to 8, I have, um, 10 over. Could I do 30 minus 20? Um, and that would be over to which gives me two and 1/2 feet. Who second. So then, if I average those two, if I average those two to get right at six, if I average those two, I would have on five over to which is 2.5 feet per second. Okay, but if I did from, um, two toe eight seconds. Um, right, because we're doing the average. And then we did the average, and then we did 48. Give me that. Um, then 2 to 8 seconds, we would get 30 minus 10 over six, which would be 20 over six. Um, which would give me 10 over three, which is, um, 3.333 feet per second. So, um, so you have to be careful. Um, so, yes, as long as my increments are the same. And that's that time you're looking for is right there in the middle. But if you don't, the answer's gonna be no