Question

Table t in seconds 0 10 15 25 30 40 45 20 35 v(t) in feet per second 274.27 179.23 141.4 108.83 80.80 56.68 35.91 18.04 2.65 223.19 Table II t in seconds 4. 5 14 15 24 25 34 35 44 45 232.8 v(t) in feet per second 223.19 148.52 39.82 35.91 5.55 141.4 86.08 80.80 2.65 Part ll: Analysis of Data Applying Integrals Calculating total change (distance traveled) of the aircraft. Using the data in Table I, use a right-endpoint estimate to calculate the distance traveled by the aircraft from t 0 to t 45 seconds Using the data in Table I, use a left-endpoint estimate to calculate the distance (total change) traveled by the aircraft from t 0 to t 45 seconds. Find the best estimate for the distance traveled by the aircraft from t 0 to t 45 seconds. A. 1 2 3 В. Graphing the model. Using the velocity data in Table I, generate a table of estimates that represents the total change of the moving object. Then, use this table of values to graph the model for the velocity function and the distance function. 15 25 30 40 45 tin seconds 10 20 35 v(t) in feet per second 80.80 2.65 274.27 223.19 179.23 141.4 108.83 56.68 35.91 18.04 s(t) C. Discuss the relevance of these graphs, and how the velocity graph is used to find the distance traveled by the aircraft. Discuss the relationship between the two graphs using calculus terminology.

Answer 1

Table 25 2-0 30 35 15 223 19 23414 .33/9u-3o 56115.9 04 2.65 v(t) 274.2 Usin ght-end pPont appuaun, Cvightad point 24.27 24.23 20 insnbed Tectamg les width hi Now eshmotd axeas ea (: A eetanle - 213.19 x)( 134.23 x 5)+ G41. 4x S) t(3 83 a5) (090x5) 6.69x ) 55.91x S) t G2.04 K5) t (2.65KS) -5(223-19+ {39.23+141.44 IG3 33+ 3030 S6- 68435,9/ S(Bu63) 4233.65 4eJ3.65 ft . Totul chstance travelle d h i Usin last end pant appr mmakion, (Atndpoin heig hb) A :5( 274.2 1 Ll319t R79. 23+141,4 lo3.33+20 80 fS0.69 .9t 18.04) SCIS-35 : 5591.15 Totl distance travelud hre is 5591.15 tt

14.4 (o313 3-2 lc 0 3) Te bet eshmg fe ahw esn above bwo corll be jht-end approi Because, for o decreag na hon curve Raft-end appimahn prfor yht-tud a locst Ri bis bnd pw blem. wil give ou ovet-estimahon. So we can velaly dictance - imL 3S v(t 74.24 |LLb.19|179.2144o333 3u. 30 J6.693591 1 .04 E6 sCE S.15396.15 4|S44 MIST 404 233.89|143.64 0. 2 |3,15 30 30 veleaky Q65 O ->Hn (s) --t 233.ly

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