Terminal Velocity

Definition of Terminal Velocity

Terminal velocity is the constant maximum speed that an object reaches when falling through a fluid, such as air. At this speed, the forces acting on the object are balanced, so it no longer accelerates and continues to fall at a steady speed.

When an object first starts to fall, it accelerates due to gravity. As its speed increases, the resistance from the air (air resistance) also increases until it exactly balances the weight of the object. At this point, the resultant force is zero, and the object moves at terminal velocity.

Forces Involved

Two main forces act on a falling object:

• Weight (gravity): The downward force due to gravity, calculated by $W = mg$, where $m$ is mass and $g$ is gravitational field strength (approximately 9.8 N/kg on Earth).
• Air resistance (drag): The upward force caused by air pushing against the object as it moves through it. This force increases with speed.

At terminal velocity, these forces are equal in size but opposite in direction, so the resultant force is zero:

$$\text{Weight} = \text{Air resistance}$$

Because the forces balance, the object stops accelerating and continues falling at a constant speed.

For example, a skydiver jumping out of a plane initially accelerates downwards because weight is greater than air resistance. As speed increases, air resistance grows until it balances weight, and the skydiver reaches terminal velocity.

Factors Affecting Terminal Velocity

Terminal velocity depends on several factors that affect the balance between weight and air resistance:

• Mass of the object: A heavier object has a greater weight, so it requires a larger air resistance to balance it. This usually means a higher terminal velocity.
• Shape of the object: Streamlined shapes experience less air resistance, so they tend to have higher terminal velocities. Objects with irregular or flat shapes experience more drag, lowering terminal velocity.
• Surface area: A larger surface area increases air resistance, reducing terminal velocity. For example, a parachute increases surface area dramatically to reduce terminal velocity and slow descent.
• Air density: Terminal velocity is lower in denser air because air resistance is greater. For example, terminal velocity is slightly different at sea level compared to high altitudes.

Understanding these factors helps explain why different objects fall at different speeds and why safety equipment like parachutes work.

Representing Terminal Velocity

Terminal velocity can be shown clearly on a velocity-time graph:

• The graph starts with a curve upwards, showing acceleration as the object speeds up.
• The curve flattens out to a horizontal line, indicating the object has reached a constant velocity — the terminal velocity.

This plateau means acceleration is zero because the forces balance.

Similarly, a force versus velocity graph shows how air resistance increases with velocity:

• At zero velocity, air resistance is zero.
• As velocity increases, air resistance increases until it equals the weight.
• The point where air resistance equals weight corresponds to terminal velocity.

These graphs help visualise how forces and velocity change during free fall.