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Math Help - Newton’s second law

  1. #1
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    Newton’s second law

    Suppose an object traveling through a fluid is subject only to a force resisting its motion, and this resisting force is proportional to the velocity of the object. By Newton’s second law we have m(dv/dt)=-cv. Find a solution v(t) of this differential equation for which v(0) = v sub 0.
    Last edited by mikegar813; September 22nd 2009 at 11:09 AM.
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  2. #2
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    Quote Originally Posted by mikegar813 View Post
    Suppose an object traveling through a fluid is subject only to a force resisting its motion, and this resisting force is proportional to the velocity of the object. By Newton’s second law we have m(dv/dt)=-cv. Find a solution v(t) of this differential equation for which v(0) = v0.
     <br />
m \frac{dv}{dt} = -kv<br />

     <br />
\frac{dv}{dt} = -\frac{k}{m}v<br />

    rate of change of velocity is directly proportional to itself ...

     <br />
v = v_0 \, e^{-\frac{k}{m}t}<br />
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    I don't even know where to begin with this one.
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    As Skeeter said, you have \frac{dv}{dt}= -\frac{k}{m}v.

    Separate that into "differentials": \frac{dv}{v}= -\frac{k}{m}dt.

    Now integrate both sides and then solve for v.
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  5. #5
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    ok thanks
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