1. Here's the storyI of how I came to wori: one day last semester. I've just reached the main road near my house when I decide to set myself a challenge in preparation for an assignment In Calculus II. I decide I'm going to try to drive at a constant speed all the vvay to work. I set my speed at St] mph, well within the speed limit for the road I'm traveling on, of course. and keep on going. Amazingly, I don't hit a single trafc light and I'm able to keep on driving at this constant speed for 3D minutes. At the 33-minute mark. I've reached Leeslaurg, WI. and there is an abrupt slowdown - so alanpt. you can assume that it oocurs instantaneously. All of a sudden, I'm driving at 4i] mph and I iteep going at this constant speed for another 15 minutes. At the 45-minute maric. crisis hits! I'm almost out of gas! I decide I'd better go back to the gas station I passed on the side of the road a few minutes ago. Assume that I'm able to click my fingers and turn the car around instantaneously. I travel in the opposite direction for 15 minutes at a constant speed of St] miles per hour. For the purpose of this assignment. assume that I click my fingers again and instantly, the gas tank is filled and I'm back on the road, this time. traveling at so miles per hour for the last 3i] minutes of my JourneyI to woric. Here is the graph of my veloch over the entire journey where velocity. on the y-axis, is in miles per hour. and time, on the it-axis. is in hours. Note that I am taking \"To Work\" to he the positive direction, and "Away from Work\" to be in the negative direction. a. How many miles do Itravel at 5B miles per hour for a half an hour? How does this relate to a certain area under the graph of em above? Shade it. la. lIL'onsider the remaining segments of the journey and calculate how far I travel in each segment i.e. How about when I'm going at so miles per hour for a quarter of an hour? Etc How do these distances relate to certain areas on the graph? Shade them in. c. What tl distance have I traveled by the time I hit the 45minute mark of my journey? d. A related question: If we take my position, 5 to he i] at the main road near my house, and \"To Work\" is the positive direction, what 993?!ng am | at right now, after being on the road for 45 minutes? e. What total distance do I travel over the entire journey? f. What position am I at, at SCI minutes? How far is Hood from my house? g. Considering my overall Journey so far from home to work, how does the distance I have traveled relate to the areas you have shaded under the graph? It may help to give these areas names A, B, C, D. {Write an expression for the total distance In terms of the areas A, B, (2, I1] h. Again, considering my overall Journey so far, write down a formula for calculating my overall change in asition from beginning to end, in terms of the areas A, B, C. D. {Write an expression for the total change in position in terms of the areas A, B, C, D.)