What Determines Terminal Velocity in Free Fall? | Physics Explained

Question:

What determines the terminal velocity of a body in free fall?

Answer:

Terminal velocity is the **maximum velocity** an object can reach while falling through a fluid (like air), where the **net acceleration becomes zero**. This occurs when the **upward drag force** equals the **downward gravitational force** acting on the object.

🌐 Understanding the Forces at Terminal Velocity

The **drag force** acting on an object moving through air is given by the equation:

F_D = (1/2) × ρ × v² × C_D × A

ρ = density of the fluid (air)
v = velocity of the object
C_D = drag coefficient (depends on shape)
A = surface area presented to the airflow

⚖️ Condition for Terminal Velocity

At terminal velocity v_t, the drag force equals the weight (gravitational force):

(1/2) × ρ × v_t² × C_D × A = m × g

Solving for v_t (terminal velocity) gives us a value based on mass, surface area, and air resistance parameters.

📌 Key Insight:

The **surface area (A)** presented to the airflow plays a major role. A larger surface area increases the drag force, which in turn leads to a **lower terminal velocity**, all else being equal.

✅ Final Answer:

b. the surface area presented to the airflow

🔍 Conclusion:

Terminal velocity is not simply a function of speed—it is a result of the **balance between gravity and drag**. The shape and orientation of the falling object (which affects surface area), the air’s density, and the object’s mass all contribute. Among these, **surface area** significantly impacts how quickly the drag force builds up, thus determining how fast the object will fall before reaching terminal velocity.

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