First, let me preface this question that I have been out of academia for about 5 years now, and am just starting to get back into it, although it seems my Calc/Kinematics is a little rusty.(adsbygoogle = window.adsbygoogle || []).push({});

b]1. The problem statement, all variables and given/known data[/b]

An object of weight W is falling through a medium such that the object's drag force is proportional to its velocity. Express the velocity in terms of time if the initial velocity of the object is zero.

2. Relevant equations

F=ma

F=KV

a=dV/dt

3. The attempt at a solution

Ok, so just from the problem statement alone, I know we have an object on which two forces are acting; the weight of the object due to gravity and the drag force on the object.

Fnet = mg - KV

Since g is always a constant, it's the acceleration of the drag force we are trying to solve for, correct? Since F=KV, and F=ma, by association we have ma=KV, or a=KV/m, so now we have a function of acceleration in terms of velocity. If we plug this into a=dV/dt, we end up with:

KV/m = dV/dt

or

dt = (m/KV)dV

Integrating both sides, we end up with:

[itex]\int[/itex]dt = (m/K)[itex]\int[/itex](1/V)dV or t = (m/K)ln(V)+C

Now if we solve for V in terms of t we get:

ln(V) = (tK/m)-C or V = e^[(tk/m)-C]

So this is as far as I have been able to get with this problem, because when you plug in initial velocity to solve for C, you get 0 = e^(0-C), but e^x is undefined when x = 0.

Am I making a wrong assumption at the beginning of the problem? I've got about 6 pages of scratch work and I feel this is the closest I've gotten to the actual solution. Any advice would be helpful. Thanks in advance.

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# Homework Help: Kinematics of Falling Object

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