Terminal Velocity derivation: Overview, Questions, Preparation

The highest speed or velocity that any object can attain while passing through a fluid is called the terminal velocity. When the sum of buoyancy and force is equal with the gravity of the force acting on it, the terminal velocity is observed. When an object’s speed increases, the drag force working on it also increases with it; however, it depends on the substance as well. The gravitational force and drag force at any point in time will restrict the speed and add a delay in the velocity because of the gravitational pull of the subjected substance. 

Buoyancy at a point is low. When the objects’ acceleration stops and starts to fall at a constant rate, the thermal velocity is defined. The thermal velocity can be seen in skydiving because of the free-falling property. 

Mathematically, the terminal velocity is calculated as:

Vt = √2mg/pACd

Here, Vt is terminal velocity;

m is the mass of the object;

g is the acceleration;

p is the density;

A is the area projected ;

Cd is the drag coefficient.

The following derivation will make it clear in the context of terminal velocity:

F = bv2 (drag force).

b is constant; it depends on the drag types

ΣF = ma (free fall of an object).

mg-bv2 = ma (this is an assumption that it falls in positive direction)

mg- bv2 = m (dv/dt.). (1/m) dt = dvl (mg – bv2)

(differential form of equations)

Terminal Velocity in the Buoyancy Force Presence

When the terminal velocity is optimised, or the weight of the object is reached, it balances the buoyancy force and drag force, i.e.,

W = Fb + D

Here, W = weight of the object;

Fb = buoyancy force;

D = drag force.

The chapter ‘Introduction to Motion’ holds a weightage of 6 marks and consists of 2 short questions and one very short question of 2 and 1 mark, respectively. The topic ‘Terminal Velocity’ is of great importance in this concept and might come as a short question of 3 marks. 

1. Explain the derivation of terminal velocity.

Vt = √2mg/pACd

Here, Vt is terminal velocity;

m is the mass of the object;

g is the acceleration;

p is the density;

A is the area projected;

Cd is the drag coefficient.

2. Explain the equational relation between drag force and terminal velocity.

The following derivation will make it clear in the context of Terminal velocity:

F = bv2 (drag force)

3. Explain the differential form of the equation for terminal velocity.

mg- bv2 = m (dv/dt.). (1/m) dt = dvl (mg – bv2)

(differential form of equations)

Q: What do you mean by terminal velocity?

Q: When is terminal velocity observed?

Q: What’s the effect of gravitational pull on terminal velocity?

Q: What’s the effect of buoyancy pull on terminal velocity?

Q: How to calculate terminal velocity in a buoyant force?