 # Terminal Velocity

Terminal Velocity is the highest velocity that is achieved by an object as it falls through a fluid or a gas. For instance air but it is applicable equally to all liquids. Terminal force occurs when an object is subjected to a resistance that increases with the increase in velocity and when its resistance equals the driving force. An object that is moving downwards with a higher speed compared to terminal velocity will eventually slow down with the terminal velocity.

Example For instance, when a person jumps out of a plane, they tend to gain speed and they move faster. The reason is the weight force that causes them to accelerate towards the ground. As mentioned earlier drag force increases with the increasing speed. The same holds true for any type of friction. Hence as the SkyDrive moves with more speed the more drag force he would possess. It continues until the net force of a skydiver is zero implying that he is no longer accelerating. This states that he has reached terminal velocity. He would continue with this same speed until he opens his parachute.

## Mathematical Representation of Terminal Velocity

Terminal Velocity is stated as follows;

$V_{t}= \sqrt{\frac{2mg}{ho\ AC_d}}$
• Where A represents the projected area of any object.
• ‘m’ represents the mass of the falling object.
• ‘g’ represents acceleration due to gravity.

### Derivation Of Terminal Velocity

According to the drag equation,

$F_{net}=ma=mg- \frac{1}{2} pv^{2}AC_d$

F=0 at Equilibrium,

$mg- \frac{1}{2}pv^{2}AC_{d}=0$

From solving this, we get

$V_{t}= \sqrt{\frac{2mg}{ho\ AC_{d}}}$

### Calculation Of Thermal Velocity

Find the mass of the falling object. It should be measured in the metric system. That is it should be measured either in kilograms or in grams. Suppose if you are using the imperial system make sure of the units.

Determine the acceleration due to gravity. Now calculate the downward pull of the gravity. That is F=MA. Whereas in the case of imperial systems, it is termed lfb of the object which is commonly termed as weight. It is one of the methods of calculating the thermal velocity.