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27 January, 06:21

The position of an object moving vertically along a line is given by the function s (t) = - 16t^2 + 128t. Find the average velocity of the object over the following intervals.

a. [1, 4]

b. [1, 3]

c. [1, 2]

d. [1, 1 + h], where h > 0 is a real number

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  1. 27 January, 06:48
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    a) 48

    b) 64

    c) 80

    d) 96-16h

    Step-by-step explanation:

    a) s (1) = 112 and s (4) = 256

    average velocity on [1,4] = (256-112) / (4-1) = 48

    b) s (1) = 112 and s (3) = 240

    average velocity on [1,3] = (240-112) / (3-1) = 64

    c) s (1) = 112 and s (2) = 192

    average velocity on [1,2] = (192-112) / (2-1) = 80

    the next one's tricky to type. watch the parentheses carefully:

    d) s (1) = 112 and s (1+h) = - 16 (1+h) ^2 + 128 (1+h)

    average velocity on [1,1+h] =

    (s (1+h) - s (1)) / ((1+h) - 1) = (-16 (1+h) ^2 + 128 (1+h) - (112)) / h

    = (-16 (1+2h+h^2) + 128+128h - 112) / h

    = (-16 - 32h - 16h^2 + 16 + 128h) / h

    = (96h - 16 h^2) / h

    = 96 - 16h
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