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  1. #1
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    velocity Question

    if s = 2t^3 - 5t^2 - 2 and t=2, is s increasing or decreasing?

    i don't really get what im supposed to do here. how do i find which one it is?
    i know how to find avg. V (or V) and avg. a (or a), but what do i do here?

    thanks for any help, this question is stumping me
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  2. #2
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    Quote Originally Posted by mneox View Post
    if s = 2t^3 - 5t^2 - 2 and t=2, is s increasing or decreasing?

    i don't really get what im supposed to do here. how do i find which one it is?
    i know how to find avg. V (or V) and avg. a (or a), but what do i do here?

    thanks for any help, this question is stumping me
    if s(t) is increasing, then s'(t) > 0

    if s(t) is decreasing, then s'(t) < 0

    so ... find s'(2) and answer the question.
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  3. #3
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    Quote Originally Posted by mneox View Post
    if s = 2t^3 - 5t^2 - 2 and t=2, is s increasing or decreasing?

    i don't really get what im supposed to do here. how do i find which one it is?
    i know how to find avg. V (or V) and avg. a (or a), but what do i do here?

    thanks for any help, this question is stumping me
    Hi mneox,

    You have 2 choices,
    depending whether you have covered differentiation or not.

    Differentiation:

    calculate the derivative

    \frac{d}{dt}=f'(t)=\left(2t^3-5t^2-2\right)=6t^2-10t

    Now evaluate f'(2)

    f(t) is increasing if f'(t) >0
    f(t) is decreasing if f'(t)<0


    Alternative

    Work with the graph and examine f(2).
    See attached sketch.
    Attached Thumbnails Attached Thumbnails velocity Question-cubic.jpg  
    Last edited by Archie Meade; February 23rd 2010 at 05:27 PM.
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  4. #4
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    Quote Originally Posted by skeeter View Post
    if s(t) is increasing, then s'(t) > 0

    if s(t) is decreasing, then s'(t) < 0

    so ... find s'(2) and answer the question.
    Ohh okay, thank you very much.

    I also want to ask, does a particle reverse its direction every time there is a root?
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  5. #5
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    Quote Originally Posted by mneox View Post
    Ohh okay, thank you very much.

    I also want to ask, does a particle reverse its direction every time there is a root?
    a particle reverses its direction every time s'(t) = v(t) changes sign.
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