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Math Help - Velocity and position

  1. #1
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    Velocity and position

    If s(t) = (1/3)(t^3) - (3/2)(t^2) - 18t
    During what time is the object moving towards the origin?
    I know I set s(t)v(t) < 0, but from there on Iím a little stuck.

    When the velocity is 10m/s, find its displacement.
    My answers to this were : -511/6, and 208/3
    Is this correct?

    How many times does the object cross a marker on the line located at s = 20?
    Iím not sure how to do this one.

    Any help is appreciated.
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  2. #2
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    Quote Originally Posted by Shapeshift View Post
    If s(t) = (1/3)(t^3) - (3/2)(t^2) - 18t
    During what time is the object moving towards the origin?
    I know I set s(t)v(t) < 0, but from there on I’m a little stuck.

    When the velocity is 10m/s, find its displacement.
    My answers to this were : -511/6, and 208/3
    Is this correct?

    How many times does the object cross a marker on the line located at s = 20?
    I’m not sure how to do this one.

    Any help is appreciated.
    \frac{ds}{dt} = v < 0 \Rightarrow t^2 - 3t - 18 < 0 \Rightarrow (t - 6)(t + 3) < 0.

    A graph of v = (t - 6)(t + 3) makes it clear that the object is moving to the left for 0 < t < 6 and moving to the right for t > 6.

    Now note that at t = 0 the object is at s = 0.
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  3. #3
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    so for the last question where i have to find how many times the object crosses s=20

    i set s(t) = 20, giving me 20 = (1/3)(t^3) - (3/2)(t^2) - 18t

    after bringing the 20 over and finding the lowest common denominator, i get

    2t^3 - 9t^2 -108t -120 = 0

    i tried using the factor theorem, but nothing seems to work out.
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  4. #4
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    Quote Originally Posted by Shapeshift View Post
    so for the last question where i have to find how many times the object crosses s=20

    i set s(t) = 20, giving me 20 = (1/3)(t^3) - (3/2)(t^2) - 18t

    after bringing the 20 over and finding the lowest common denominator, i get

    2t^3 - 9t^2 -108t -120 = 0

    i tried using the factor theorem, but nothing seems to work out.
    Are you allowed to draw a graph to answer the question ....? If so, it's clear that there's only one value of t greater than zero.
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