Velocities of the 2 cars during the race are given in the tables below where velocities, v are in miles per hour and times t are in seconds.
Sappho's car:
time: 0 1 2 3 4 5 6 7 8 9 10
velocity:0 20 35 48 62 75 85 93 99 106 111
Homer's car:
time: 0 1 2 3 4 5 6 7 8 9 10
velocity: 0 18 31 43 58 68 79 86 93 95 96
A. Use ten trapezoids to approximate the area between the curves y = vs(t) and y = vH(t) (s and H for sappho and homer) on the interval from t = 0 to t = 10. What definite integral are you approximating?
B. If you haven’t done so, convert your answer from part A into units that make good
common sense for the physical situation described. Then explain what practical meaning
this answer has for the physical situation.
C. Estimate the average velocity of Sappho’s car over the 10-second interval using 5
subintervals and midpoints.

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  1. A. Geez, the trapezoids all have height 1, so the area of each is just the average of the two y-coordinates.

    B. think of the units on the axes: v * t = distance

    C. avg speed is totaldistance/totaltime

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  2. ummm
    could you please be more specific?

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