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Math Help - Solving for a derivative - Question for an assignment

  1. #1
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    Solving for a derivative - Question for an assignment

    New to the forum, and ofcourse I type in Math help and up pops this great place!

    I have an assignment due tomorrow and I cannot figure out this question... It is basic calc but not taking calc for over 10 years, I am rusty.

    Could someone give me a hand with this question!!

    Given the following equation for displacement:

    S =So + VoT - 1/2(AT)2 ; Where So, Vo and A are constants.

    Use the equation for the derivative to find V from the derivative of the displacement, and then A, from the derivative of velocity.



    Any help with this would be great - If it can be broken down into steps so I can understand?

    Thank you kindly....


    -One frustrated student.

    Jeff
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    Re: Solving for a derivative - Question for an assignment

    I think the A should lie outside the parentheses (as in, -\frac{1}{2}At^2).

    Find dS/dt:

    \frac{dS}{dt} = V - At \Rightarrow \frac{dS}{dt} + At = V.

    Differentiate again to find A.
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  3. #3
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    Re: Solving for a derivative - Question for an assignment

    To further this, I know you have to get the prime of S which will cancel out a bunch of the characters, but I am stuck with breaking that down.

    To get the A... I am unsure. A friend mentioned to get the prime of the prime, but I am not sure if that is how to do it.
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  4. #4
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    Re: Solving for a derivative - Question for an assignment

    Quote Originally Posted by richard1234 View Post
    I think the A should lie outside the parentheses (as in, -\frac{1}{2}At^2).

    Find dS/dt:

    \frac{dS}{dt} = V - At \Rightarrow \frac{dS}{dt} + At = V.

    Differentiate again to find A.
    THere is actually no brackets at all in the question as I placed there, but yes, you would be correct. I put them there to show the multiplication.

    Can you please explain the above... I am looking forward to my calc tutor...
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    Re: Solving for a derivative - Question for an assignment

    Basically what I did was differentiate both sides with respect to time (t). This is because, if X = Y, then dX/dt = dY/dt.

    The LHS just becomes dS/dt. For the RHS, you can differentiate by finding the derivatives of each of the terms and then adding them up.

    \frac{dS}{dt} = \frac{d}{dt}S_0 + \frac{d}{dt}(V_0t) - \frac{d}{dt}(\frac{1}{2}At^2)

    The derivative of a constant ( S_0) is zero. d/dt of any constant times t, is just that constant, so \frac{d}{dt}(V_0t) = V_0. The derivative of any expression in the form At^n is just Ant^{n-1} (look up "power rule").

    Therefore, \frac{dS}{dt} = 0 + V_0 - \frac{1}{2} (2At) = V_0 - At
    Thanks from Hearzy
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    Re: Solving for a derivative - Question for an assignment

    Quote Originally Posted by Hearzy View Post
    THere is actually no brackets at all in the question as I placed there, but yes, you would be correct. I put them there to show the multiplication.
    Also, you should just skip the brackets. (At)^2 and At^2 mean entirely different things.
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  7. #7
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    Re: Solving for a derivative - Question for an assignment

    Richard,

    Thank you kindly for your help - Next time I will drop the brackets... I see what I did there now. Thank you for questioning that...

    I will be reviewing this in the morning but what you have wrote out does make sense. A bit of practice will go a long way.

    Congrats on post 500 as well! Well deserved - Now how do I give a thumbs up?

    -Jeff
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    Re: Solving for a derivative - Question for an assignment

    Huh, didn't even notice my 500th post

    You're welcome.
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