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Shown is the graph of a force function (in newtons) that increases to its maximum value and then remains constant. How much work is done by the force in moving an object a distance of 8 m?

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Applications of Integration

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Baylor University

University of Michigan - Ann Arbor

Idaho State University

Boston College

sean is the graph of a force function in mutants. That increases to its maximum value and then remains constant. So this is the maximum value we can see here. Right. Then after that it remains constant. That this force forces in the vice by access straight. No. Then it is asked that how much work is done by the fourth in moving an object a distance of eight m. So let's say this is this graph. We know that this is a graph, right? Mhm. No, we can say that work done is given by the expression work as equals to force into displacement. And if we integrate then we will get the work done. Right? So here why we are integrating milk? Because the the graph what between force and displacement is given to us and the area covered by it will be worked on. Right? So this is one triangle. This this graph is made of two. Do you can say two things. What one is this triangle and another is this rectangle. So we know the area of triangle as well as the rectangle. So this is a right angle triangle. Yes. So we can say let us say the strangle has area even. And this has a two. Right? So even plus a two will be equal to what Have in two ways into hide for right angle triangles. So for right angle triangle half in two bases work. This is nothing. But this is four. And this is 24. This height is 24 because 24 is given to us here. Right? So four into 24. So this will be area for even that. That is triangle. For this triangle. Now, what rectangle? We will find out lengthen to breath. We know the area is lent into bread simply. So length is work, length is 8 -4. That is four only. Or you can count it from here. 1234. Right? So four units is the Lynn you can see uh bread. Right? And it's this length is word or you can say this is length four. Most dreams for you. Okay? plant is you can say 24, right? And this you can say this is for All right. Or you can write eight minus course with this, this part. This party this is excluded. So, in units that the tangle has bread or better four units. No, There was all this. And we will be getting 48 years less 96. This will give us 1 44 units. So this is the work done. Mhm. So, you can see, Okay, this will be in jewels. Right? You can see Newton meter. You can right here. So, you can say 144. Newton. Newton is the answer for this question. I hope your industry concept. Thank you for watching