B Mastering Equation Solving: m(dv/dt)=mg-bvn | Step-by-Step Guide

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The discussion centers around the equation m(dv/dt) = mg - bvn, which raises questions regarding its validity and dimensional consistency. Participants express confusion over the symbols and their meanings, suggesting that the equation might represent a differential equation related to a falling body with resistance proportional to velocity raised to a power. There is a suggestion that the equation may need to be reformulated to m(dv/dt) = -mg - bvn for clarity. The conversation also touches on the integration of a related equation, dx/dt = 1 - axn, indicating that further context is needed to fully understand the original equation's implications. Overall, the thread highlights the complexities of interpreting and solving differential equations in physics.
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m (dv / dt) = mg-bvn
 
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Opressor said:
m(d2v/dt2)=-mg-bvn
This equation doesn't make sense if the symbols have their usual meanings. Did you mean m(dv/dt)=-mg-bvn ?
 
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What does it represent? It is a differential equation (second derivative of velocity?) equals -(mass)(gravity?) - (some number b) times (velocity?)^n
If I am even close, it does not look like the dimensions match.
 
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is the equation of a falling body having as resistance force bv ^ n
 
It looks like you are asking about solutions to dx/dt = 1 - axn? For a and n = constants you can just integrate it, so I guess there is more to your equation than we understand?
 
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Assume that this is a case where by sheer coincidence, two sources of coherent single-frequency EM wave pulses with equal duration are both fired in opposing directions, with both carrying the same frequency and amplitude and orientation. These two waves meet head-on while moving in opposing directions, and their phases are precisely offset by 180 degrees so that each trough of one wave meets with the crest of the other. This should be true for both the electric and magnetic components of...
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