I'm working on a small java program, and I was wondering if there was an equation to calculate the approximate velocity of a falling body, in function to its mass $M$ and the time $t$ since the beginning of the fall (example; Body $A$ of a mass of 57kg has a velocity of $y$ after 11 seconds of fall) I googled it and the only equations I found were either in function of time or mass, but never both. Sorry if this comes out as a rudimentary question, I'm a computer science student, my last physics course was in high school.
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Gravitational field strength on earth is 9.8m/s^2 so I think you can just rearrange the acceleration equation which is a = ∆v/t So 9.8 = ∆v/11 so ∆v=9.8*11. Velocity in a falling object isn't affected by its mass, hope this helps.
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The simplest thing you could perhaps do to model the motion on a more practical level would be to introduce a damping term $−bv$. Already you will see an asymptotic velocity here and an explicit dependence of $v$ on $m$ and $t$, as one would expect.
So, instead of solving $m \dot{v} = mg$ in vacua solve $$m \dot{v} = mg - bv,$$ a step up in description accounting for resistive forces. You will find something like $$v = \frac{mg}{b} \left(1 - \exp(-bt/m) \right)$$ with asymptote $mg/b$ as $t$ gets large.
Depending on the details of the object, it may be preferable to describe the damping instead with a $-bv^2$ dependence etc
CAF
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Assuming you are in earths gravitational field, an equation of time and mass will end with the mass cancelled, so it's irrelevant to the calculation.
Otherwise: $$v_f=v_0+t*\frac{Gm_om}{r^2}$$ where $m_o$ is the mass of the planet or body you're on.
mcchucklezz
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