1. 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.

2. Originally Posted by mikegar813 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.
$\displaystyle m \frac{dv}{dt} = -kv$

$\displaystyle \frac{dv}{dt} = -\frac{k}{m}v$

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

$\displaystyle v = v_0 \, e^{-\frac{k}{m}t}$

3. I don't even know where to begin with this one.

4. As Skeeter said, you have $\displaystyle \frac{dv}{dt}= -\frac{k}{m}v$.

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

Now integrate both sides and then solve for v.

5. ok thanks

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