# Terminal velocity

## Explanation

Terminal velocity is the maximum velocity that a free-falling object can reach and stop accelerating further. When an object falls under the influence of gravity, the resistance due to the presence of air molecules creates drag. As the object keeps accelerating the drag increases proportionally and reaches a point where the drag force balances the weight of the falling object. Sometimes, if the object has a buoyant force, it is added up to the forced caused due to drag. At this point, the object can no longer accelerate and reaches the constant velocity, known as the terminal velocity.

At terminal velocity, the gravitational force acting on it is equal to the force of drag exerted by the fluid. Mathematically, terminal velocity can be formulated by analyzing the total force acting on it.

${\displaystyle F_{total}=F_{gravity}-F_{drag}}$

${\displaystyle F_{total}=ma}$, ${\displaystyle F_{gravity}=mg}$, ${\displaystyle F_{drag}={\frac {1}{2}}\rho v^{2}AC_{d}}$

At terminal velocity, the total force acting on the object will be zero.

${\displaystyle mg={\frac {1}{2}}\rho v^{2}AC_{d}}$

Where ${\displaystyle m}$ is the mass of the object, ${\displaystyle g}$ is the acceleration due to gravity, ${\displaystyle \rho }$ is the density of the fluid, ${\displaystyle v}$ is the terminal velocity, ${\displaystyle A}$ is the surface area, and ${\displaystyle C_{d}}$ is the coefficient of drag.

 ${\displaystyle V_{terminal}={\sqrt {\frac {2mg}{\rho AC_{d}}}}}$