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14 November, 11:51

The position of an object moving along a straight line for

t 0 is given by s1 (t) = t3 + 2, and the

position of a second object moving alongthe smae line is given by

s2 (t) = t2. If bothobjects begin at t = 0, at

what time is the distance between theobjects a minimum?

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  1. 14 November, 12:12
    0
    at 2/3 seconds

    Step-by-step explanation:

    S1 (t) = t³ + 2

    Average speed, dS1/dt = 3t²

    S2 (t) = t²

    Average speed, dS2/dt = 2t

    The distance between the objects is

    dS1/dt - dS2/dt

    = 3t² - 2t

    The time the distance between the two object is at minimum is when the distance is 0

    That is, when

    3t² - 2t = 0

    t (3t - 2) = 0

    t = 0 or 3t - 2 = 0

    t = 0 or t = 2/3
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