Knowledge Organiser: Terminal Velocity

Key Terms

• Terminal velocity — constant speed when drag = weight
• Drag — resistive force opposing motion through a fluid
• Resultant force — net force after all forces added
• Weight — W = mg (downward gravitational force)
• Streamlining — shape designed to reduce drag

The Sequence to Terminal Velocity

1. Weight > drag → resultant force down → acceleration
2. Speed increases → drag increases
3. Resultant force decreases → acceleration decreases
4. Weight = drag → resultant = 0 → acceleration = 0
5. Constant velocity = terminal velocity

V-T Graph Features

• Steep curve → decreasing curve → horizontal line
• Gradient = acceleration
• Area under graph = distance
• Parachute opening: steep negative gradient → new lower horizontal line

Factors Affecting Terminal Velocity

• Larger surface area → lower terminal velocity
• More streamlined → higher terminal velocity
• Greater weight/mass → higher terminal velocity
• Denser fluid → lower terminal velocity

Key Equations

• At terminal velocity: weight = drag force (resultant force = 0)
• F = ma (before terminal velocity, resultant force causes acceleration)
• Drag force ∝ v² (drag increases with the square of speed)
• W = mg (weight in Newtons from mass and gravitational field strength)

Common Mistakes

• Saying the object stops accelerating because forces disappear: At terminal velocity, forces are still acting — weight and drag are equal and opposite, giving zero resultant force, not zero force
• Thinking terminal velocity is the maximum possible speed: Terminal velocity depends on the specific conditions (shape, mass, fluid density) — a more streamlined object or greater mass gives a higher terminal velocity
• Confusing the velocity-time graph shape: The v-t graph for a falling object curves upward (decreasing gradient) before becoming horizontal at terminal velocity — the gradient (acceleration) decreases to zero, not the speed
• Saying drag increases linearly with speed: Drag force increases with the square of speed (∝ v²) — doubling speed quadruples drag, which is why terminal velocity is reached
• Forgetting the parachute phase on a skydiver graph: When a parachute opens, drag suddenly exceeds weight — the skydiver decelerates until a new (lower) terminal velocity is reached