What is the Velocity of a Falling Body with Friction in Freefall?

[devanlevin]

a small body, with the mass of M is dropped from an infinite height falling freefall, the air's friction on the body is defined by ==>f=-kv^2, k=const.
find the velocity after an infinite amount of time.

using Newtons 2nd law,
F=ma=mg-kv^2
a=g-(kv^2)/m

now, how do i find the velocity, i thought of integratning the acceleration, but i have a dependence on v in the acceleration..
aat first i thought it was meant to be a=g-(kt^2)/m
the answer is

v(t=>inf)---->sqrt(mg/k)
do i need to work with limits to reach this?? what must i do?

 

[LogicalTime]

<br /> m \ddot{y} = -mg + k \dot{y}^2<br />

with messy differential equations we can still often get stable state information out which is nice. The stable state will be when the mass is no longer accelerating any longer (it's hit terminal velocity). So set
<br /> \ddot{y} = 0<br />
and see what you get!

 

[devanlevin]

thanx

 

[LogicalTime]

np man, glad I could help