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## Main Question or Discussion Point

Hi everyone,

I'm a doctor who is fair at maths - haven't done physics for a while. I'm trying to model some heart physiology which I can describe as a mechanics problem:

I have a particle, mass m, with a constant force acting on it, f.

It also has resistance R, where the resistance is equal to the velocity of the particle squared times a constant k:

R = kv

my equation of motion is:

m.dv/dt = F = f - kv

I want to find the velocity after a given time. The are formula on the internet which describe a solution to this problem (mostly in the context of a falling body accelerating to wind resistance):

http://keisan.casio.com/has10/SpecExec.cgi?path=06000000.Science/01300100.Free fall/10010100.Free fall with air resistance (velocity and distance)/default.xml"

However they all assume that starting velocity is zero. I need a solution for any starting velocity. so:

t

v

f = constant force on particle

m = mass

R = resistance = kv

what would be the velocity at time t?

I know this is difficult. I'm not sure if this is really a maths problem.

kenneth

I'm a doctor who is fair at maths - haven't done physics for a while. I'm trying to model some heart physiology which I can describe as a mechanics problem:

I have a particle, mass m, with a constant force acting on it, f.

It also has resistance R, where the resistance is equal to the velocity of the particle squared times a constant k:

R = kv

^{2}my equation of motion is:

m.dv/dt = F = f - kv

^{2}I want to find the velocity after a given time. The are formula on the internet which describe a solution to this problem (mostly in the context of a falling body accelerating to wind resistance):

http://keisan.casio.com/has10/SpecExec.cgi?path=06000000.Science/01300100.Free fall/10010100.Free fall with air resistance (velocity and distance)/default.xml"

However they all assume that starting velocity is zero. I need a solution for any starting velocity. so:

t

_{0}= time 0.v

_{0}= velocity at time 0.f = constant force on particle

m = mass

R = resistance = kv

^{2}as above, where k = constant, v = velocitywhat would be the velocity at time t?

I know this is difficult. I'm not sure if this is really a maths problem.

kenneth

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