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14 August, 21:24

Suppose an object moves along the y axis so that its location is yequals f (x) equalsxsquaredplusx at time x (y is in meters, x is in seconds). Find (A) The average velocity (the average rate of change of y with respect to x) for x changing from 2 to 5. (B) The average velocity for x changing from 2 to 2plush. (C) The instantaneous velocity at xequals2 second. (A) The average velocity is 8 m/sec. (B) The average velocity is (nothing) m/sec. (C) The instantaneous velocity is 5 m/sec.

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  1. 14 August, 21:44
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    Given

    y (x) = x² + x (x represents time in seconds)

    A)

    value of y at x = 2

    = 2²+2 = 6 m

    value of y at x = 5

    = 5²+5 = 30 m

    displacement = 30 - 6 = 24 m

    Time duration = 5 - 2 = 3 s

    average velocity

    = displacement / Time duration

    = 24 / 3 = 8 m / s

    B) For x changing from x to x plus ie for small change in x:

    value of y at x = 2

    = 5

    For small change in x, the value of y will again be 5 so displacement during small change in x will be zero. Hence average velocity will be zero.

    C)

    y (x) = x² + x

    dy / dx = 2x + 1

    dy / dx represents instantaneous velocity

    so when x = 2

    instantaneous velocity = 2 x 2 + 1

    = 5 m / s
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