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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