Question

answer a-e please

A drag racer accelerates at a(t) = 86 ft/s. Assume that v(0) = 0 and s(0) = 0. a. Determine the position function for t2 0. b. How far does the racer travel in the first 5 s? c. At this rate, how long will it take the racer to travel d. How long will it take the racer to travel 300 ft? e. How far has the racer traveled when it reaches a speed of 172 ft/s? va mi? a. The position function for t20 is s(t) = b. In the first 5 s, the racer travels ft. (Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.) c. At this rate, it will take the racer s to travel mi. (Do not round until the final answer. Then round to three decimal places as needed.) d. It will take the racers to travel 300 ft. (Do not round until the final answer. Then round to three decimal places as needed.) e. When the racer reaches a speed of 172 ft/s, it has traveled ft. (Do not round until the final answer. Then round to three decimal places as needed.)

Answer 1

at =) do = 86 at uzo at Ans Given, a (t) = 86 ftlu? Now a(t) = du(t) - V = velocity -) du = 860t separate variables 5) Sdv = 586d+ → Integrate both sides -) 86t tc =) ult) = 86ttc Given U (0) 20 at tio O = 86Xo + c --) Coo : u(t) = 860 Separate variables • Now dalt) = B(t) = 866 =) doc - 866 = dsc=86t at at =) / dx = 1864 at x = 86t? Hc -) X=43++c =) s=43t2tc (I have taken s as x earlier ) Now given s (OJ =0 at t:os=o = 0 =430²tc = (zo S(t)=43t 2 @ the position function for t zo is s(t)=43t2 O first 5 sec distance = s(5) = 43x52 = 1075 Ft © To find time when s = gọi là. - 13 20ft -) 1320 =43t2 =) t 2 = 30.69 767 4418604 - t ñ 5.541 sec 2

d Time when s= 300 Ft 7) 300 543t 2 - te ~ 300 43 2.641 twhen Ult) = 172 ) 866 =172 =) t=2 5 (2) = 43x2x2 = 43x4 = 172 Ft