Question

5.1.15 Question Help The velocity of an object moving along a line is given by v 2t+4 ft/s on the interval 0sts4. a. Divide the interval [0, 4] into subintervals, [0, 1], [1, 2], [2, 3], and [3, 4]. On each subinterval, assume the object moves at a constant velocity equal to the value ofv evaluated at the midpoint of the subinterval and use these approximations to estimate the displacement of the object on [0, 4]. (See part (a) of the figure.) b. Repeat part (a) for n 8 subintervals (see part (b) of the figure). Click the icon to view the figures. a. For n 4 subintervals, the approximate displacement of the object isft. (Simplify your answer.) Figures for (a) and (b) 40- 40- 20- 20- (a) (b)

Answer 1

The velocity of an objectmoving along a line is given by v 2t +4 fls on the interval 0st4 a. Divide the interval [0, 4] into subintervals, [0, 1], [1, 2], [2, 3], and [3, 4]. On each subinterval, assume the object moves at a constant velocity equal to the value of v evaluated at the midpoint the subinterval and use these approximations to estimate the displacement of the object on [0, 4]. (See part (a) of the figure.) Th follauing tabte ves Copximate zo o tz4. computatrm ausphamut Hhe 40- Mid Point Interval Velocity Displacement [0, 1] [1, 2 [2, 3 0.5 4.5 20- 1.5 8.5 58 16.5 2.5 3, 4] 3.5 28.5 58 . For n 4 subintervals, the approximate displacement of the object is 58 ft (a) b. Repeat part (a) for n 8 subintervals (see part (b) of the figure) The felloing taa gires th computaham of apraianke dphennt in vitea o,27 urignidprsnt nattnod 10- usst8 subinkesnals Displacement Interval Mid Point Velocity [0, 0.5 0.25 4.125 [0.5, 1] 0.75 5.125 58.5 20- [1, 1.5] 1.25 7.125 [1.5, 2 [2, 2.5 1.75 10.125 2.25 14.125 [2.5,3] 2.75 19.125 [3, 3.5 3.25 25.125 [3.5, 4] 3.75 32,125 117 (b) Ptsplaceanent 58.5