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Math Help - Determine the position function given the velocity function

  1. #1
    JDS
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    Determine the position function given the velocity function

    The Velocity function is:

    v(t) = 3e-t - 2 and the initial position is s(0) = 0.

    Here are my calculations:

    s(t) = 3t(e-t) - 2t + C

    Since s(0) = 0 we have c=0, Thus,

    s(t) = 3t(e-t) - 2t + 0

    Did I do this one correct?
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    Re: Determine the position function given the velocity function

    There looks to be a mistake involving the integral of e^-t
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  3. #3
    JDS
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    Re: Determine the position function given the velocity function

    I thought as much, I was not sure how to go about doing that
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  4. #4
    JDS
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    Re: Determine the position function given the velocity function

    so then would this be correct? s(t) = 3t(et) - 2t + 0
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    Re: Determine the position function given the velocity function

    Quote Originally Posted by JDS View Post
    so then would this be correct? s(t) = 3t(et) - 2t + 0

    No it should be s(t)=-3e^{-t}-2t+3. WHY?
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    Re: Determine the position function given the velocity function

    Can you do the derivative of e^{-x}? if so think backwards and try and figure out what the integral would be.
    Thanks from JDS
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  7. #7
    JDS
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    Re: Determine the position function given the velocity function

    I do not understand.... in the question it says s(0) = 0 so would c not equal 0? and I also do not understand how you got -3e^-t.....It looks to me like the derivative of that would not be 3e^-t.......perhaps I need more coffee
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    Re: Determine the position function given the velocity function

    I suggest going back to basics and just looking up what the derivative is of a function of the type [e^{ax}] and then reasoning backwards to figure out what the integral, knowing that integration is the opposite of differentiation.
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    Re: Determine the position function given the velocity function

    Quote Originally Posted by JDS View Post
    I do not understand.... in the question it says s(0) = 0 so would c not equal 0?

    Look at reply #5. What is s(0)=~?
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  10. #10
    JDS
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    Re: Determine the position function given the velocity function

    thanks, to both of you, and I did just that rousseau, sometimes all this calculus just jiggles around for me lol, but I do see, now, how the derivative of e^-x would in fact equal -e^(-x)..thanks! so that now makes since.....

    -3e^-t - 2t + C However I still am unsure why you got a 3 in place of the C(Constant) when the constant was defined as 0 (at least for the starting point)

    Sorry if I sound like an idiot, teaching calculus to oneself is quite a task!
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  11. #11
    JDS
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    Re: Determine the position function given the velocity function

    correction, I guess I am no longer teaching myself, you are all teaching me, which is greatly appreciated!!!
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    JDS
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    Re: Determine the position function given the velocity function

    Quote Originally Posted by Plato View Post
    Look at reply #5. What is s(0)=~?
    From what I can tell, s(0) = 0

    does it not?

    hmmmm....I just had a thought...but I could be wrong..... does it matter what C is as long as it is any constant?
    Last edited by JDS; December 1st 2012 at 11:38 AM. Reason: added a thought
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    Re: Determine the position function given the velocity function

    Quote Originally Posted by JDS View Post
    From what I can tell, s(0) = 0 does it not? I just had a thought...but I could be wrong..... does it matter what C is as long as it is any constant?

    It matters very much if we are given a initial position to start with.
    We were given, s(0)=. So the position is 0 if t=0.
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  14. #14
    JDS
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    Re: Determine the position function given the velocity function

    okay, so then you are saying that s(3) = 3 = t which makes that the constant?
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  15. #15
    JDS
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    Re: Determine the position function given the velocity function

    I understand that s(0) = 0 is the starting point, but how did we arrive at the constant being equal to 3, that is the part Im just not quite getting
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