What is Free Fall?
Free fall is motion under gravitational force alone. An object need not move downward to be in free fall—the Moon orbits Earth while in free fall, continuously pulled by gravity yet never hitting the surface because of its horizontal velocity component.
The defining conditions are:
- Gravity is the only net force acting on the object
- No air resistance opposes the motion
- Acceleration remains constant at g ≈ 9.81 m/s² on Earth
In reality, air resistance constrains falling speeds, introducing a terminal velocity. A true vacuum-free fall, however, reveals the pure kinematic behaviour described by Newton's equations.
Free Fall Equations
Two core equations govern free fall. The first relates velocity to time; the second solves for fall duration when distance is known.
v = v₀ + g·t
t = (−v₀ + √(v₀² + 2·g·h)) / g
v— Final velocity at time t (m/s or ft/s)v₀— Initial velocity at the start of fall (m/s or ft/s)g— Gravitational acceleration, typically 9.81 m/s² on Earth or 32.17 ft/s²t— Time elapsed during fall (seconds)h— Distance fallen (m or ft)
Velocity Growth in Free Fall
A falling object gains speed uniformly under constant gravitational acceleration. Each second on Earth adds approximately 9.81 m/s to the velocity, independent of the object's mass or shape.
After successive seconds:
- 1 second: 9.81 m/s
- 2 seconds: 19.62 m/s
- 3 seconds: 29.43 m/s
- 4 seconds: 39.24 m/s
This linear velocity increase is why dropping a feather and a hammer in a vacuum yields identical impact speeds. Mass is irrelevant; only time and gravity determine velocity in true free fall.
Weight and Free Fall
A common misconception holds that objects become weightless during free fall. Weight, defined as W = m·g, always acts on a body with mass. Gravity still pulls downward with full force.
What vanishes is the apparent weight—the normal force from a surface. An astronaut in orbit experiences gravity continuously but feels weightless because the spacecraft falls around Earth at the same rate. The object and its container accelerate together, so no support force is needed.
This distinction is crucial: gravitational force persists, but the sensation of weight (contact force) disappears when both object and surroundings fall in unison.
Common Pitfalls in Free Fall Calculations
Avoid these frequent mistakes when solving free fall problems.
- Confusing mass with speed — Never assume a heavier object falls faster. In a vacuum, all objects accelerate at the same rate, regardless of mass. Air resistance, not gravity, creates this illusion on Earth.
- Ignoring initial velocity — If an object is thrown downward or upward at the start, account for v₀ in your equations. Zero initial velocity is only valid for objects released from rest.
- Using the wrong value of g — Gravitational acceleration varies by location: 9.81 m/s² at sea level, less at higher altitudes, and different on other planets. Always verify which value applies to your problem.
- Forgetting air resistance limits speed — Real-world falling is capped by terminal velocity, where drag balances gravity. Physics problems often ignore air resistance, but actual skydivers level off around 50–60 m/s due to this force.