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Math Help - Have dv/dx need to find dx/dt ? (have velocity w/ respect displace - find Accel?)

  1. #1
    dtb
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    Have dv/dx need to find dx/dt ? (have velocity w/ respect displace - find Accel?)

    Hi all,
    I'm trying to figure out this problem related to motion of a spring. I know the solution but I don't know how to make it work.
    Thanks in advance

    I'm given velocity (v) = \sqrt{25-x^2} where 'x' is displacement

    Normally velocity is a function of time, so this one has really thrown me.

    I want to find a formula for Acceleration \frac{dv}{dt} which would normally be quite easy, but the above formula is Velocity as a function of x.

    I've done a bit of related rates & differentiating w/ respect other variables, but I can't figure that out for this one....

    If Acceleration = \frac{dv}{dt} = \frac{dv}{dx} x \frac{dx}{dt}

    and I know \frac{dv}{dx} (by differentiating the provided equation: ---> \frac{dv}{dx}  =  \frac{-x}{\sqrt{25-x^2}}
    then how do I find \frac{dx}{dt} please?

    (btw, using trial and error on my graphics calculator, I think the Acceleration in this case is actually inverse to the displacement).
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by dtb View Post
    Hi all,
    I'm trying to figure out this problem related to motion of a spring. I know the solution but I don't know how to make it work.
    Thanks in advance

    I'm given velocity (v) = \sqrt{25-x^2} where 'x' is displacement

    Normally velocity is a function of time, so this one has really thrown me.

    I want to find a formula for Acceleration \frac{dv}{dt} which would normally be quite easy, but the above formula is Velocity as a function of x.

    I've done a bit of related rates & differentiating w/ respect other variables, but I can't figure that out for this one....

    If Acceleration = \frac{dv}{dt} = \frac{dv}{dx} x \frac{dx}{dt}

    and I know \frac{dv}{dx} (by differentiating the provided equation: ---> \frac{dv}{dx} = \frac{-x}{\sqrt{25-x^2}}
    then how do I find \frac{dx}{dt} please?

    (btw, using trial and error on my graphics calculator, I think the Acceleration in this case is actually inverse to the displacement).
    \frac{dx}{dt}=v The derivative of position w.r.t is velcoity
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  3. #3
    dtb
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    Thanks TES.

    I think this is when I realise I've been looking at this for too long
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