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Unformatted text preview:find the position function. p ( t ) = ∫ 150 t dt= 150 + C = 75t 2 + C Again, the jet starts from rest, so it has not traveled any distance when t = 0.0 = 75(0) 2 + C t 2 2 10/27/19, 9 : 26 PM Thinkwell | Exercise Page 2 of 2http://my.thinkwell.com/twtest/exercise.cfm backanswer key next0 = 75(0) + C C = 0 So, p ( t ) = 75t 2 . Find the time it takes for the jet to reach its maximum velocity by setting v (t) = 1200and solving for t . 1200 = 150 t t = = 8 Therefore, the plane is accelerating for 8 seconds before it reaches its maximum velocity. Use the position function to findthe distance the jet travels in 8 seconds. p (8) = 75(8) 2 = 4800 So, the jet traveled 4,800 feet in the first 8 seconds. During the second stage, the jet is cruising at its maximum velocity of 1200 ft/sec. If the jet cruises for 20- 8 = 12 seconds at 1200 ft/sec, then the jet travels 12 (1200) = 14, 400 feet. Thus, the total distance the jet traveled in 20 seconds is 14, 400 + 4800 = 19, 200 feet. 1200150