# Velocity of a falling body as a function of time AND mass [duplicate]

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.

• The velocity of a falling body doesn't have anything to do with its mass (as long as it's falling a short distance in a vacuum towards something that's much bigger). The expression is $v=-gt$, where $g$ is the gravitational acceleration (9.8 m/s^2 here on Earth). – probably_someone Nov 27 '17 at 16:39
• So a pencil would fall at the same speed as a 18-ton truck? – Nihilish Nov 27 '17 at 16:41
• In a vacuum, yes. Here's some experimental evidence: youtube.com/watch?v=frZ9dN_ATew – probably_someone Nov 27 '17 at 16:42
• Wow, that's super interesting. Thanks for the info! – Nihilish Nov 27 '17 at 16:44
• @probably_someone In a practical context though, I assume the falling body would eventually reach a maximum velocity, no? I thought such a function would be logarithmic with an asymptote near the maximum value, while with v = -gt, as t approaches infinity, so does |v| – Nihilish Nov 27 '17 at 16:58

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
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.