# Distance Needed to Reach Terminal Velocity

## Homework Statement

I am completing a homework assignment that involves a python program for air resistance. One of the questions in the assignment asks us to find the minimum distance needed to reach terminal velocity. The air resistance is quadratic. The mass of the object is .5kg and its drag coefficient is .6
The gravity is normal earth gravity, 9.81m/s^2, and the initial velocity is 0m/s.

## Homework Equations

The force of air resistance=-k*v^2

## The Attempt at a Solution

I think the solution involves integrating a velocity function from time 0 to 5*time constant. However, I'm not sure how to represent the object's velocity under quadratic drag, nor am I sure of the time constant. Is it still m/k, or is it different for quadratic drag?

This is my first post! I appreciate any and all help.

The object will fall with terminal velocity when the gravitational force and the drag force become equal.
ie. mg=k*v^2
Now we know the terminal velocity
At any instant of time
F(net)=mg-kv^2
m.a(net)=mg-kv^2
m.v.(dv/ds)=mg -kv^2 (accn=v. dv/ds)
now integrate the above eqn using proper limits

Thank you very much!