# Terminal Velocity

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

Terminal velocity, abbreviated as $$v_t$$, is when an object is falling under the influence of gravity but with no other influences.

## Terminal Velocity formulas

 $$\large{ v_t = \frac { g \;d^2\; \left( \rho_p \;-\; \rho_m \right) } {18\; \eta} }$$ $$\large{ v_t = \sqrt { \frac {2 \;m \; g} {C_d \; \rho \; A} } }$$ $$\large{ v_t = \sqrt { \frac {2 \; W}{C_d \; \rho \; A} } }$$

### Where:

$$\large{ v_t }$$ = terminal velocity (maximum falling speed)

$$\large{ A }$$ = area of object

$$\large{ \rho }$$   (Greek symbol rho) = density of fluid

$$\large{ \rho_m }$$ = density of medium

$$\large{ \rho_p }$$ = density of particle

$$\large{ d }$$ = diameter

$$\large{ C_d }$$ = drag coefficient

$$\large{ g }$$ = gravitational acceleration

$$\large{ m }$$ = mass

$$\large{ \eta }$$ = viscosity of medium

$$\large{ W }$$ = weight of object