Free Fall and Acceleration Due to Gravity

Free fall is the motion of an object under the influence of gravity alone, and near the Earth’s surface all freely falling objects have the same downward acceleration, g ≈ 9.8 m/s², regardless of their mass. In brief: in free fall the kinematic equations apply with a = g = 9.8 m/s² downward. An object thrown upward is also in free fall: it slows down, stops at the top for an instant, then falls back. Air resistance is ignored in the ideal case.

Heavy and light objects fall together in a vacuum, which contradicts everyday experience with feathers and stones, where air resistance matters. This guide explains free fall and the value of g, shows how to apply the kinematic equations to falling and thrown objects, compares g on different bodies in a table, works through examples and corrects common mistakes.

What is free fall?

An object is in free fall when gravity is the only force acting on it. This includes a dropped stone, an object thrown up (on the way up and down), and an astronaut in orbit. In practice, air resistance affects light, large objects such as a feather or a sheet of paper, but for a compact dense object over a short distance, it is small. In the vacuum, a hammer and a feather fall together, as astronaut David Scott showed on the Moon in 1971.

What is the acceleration due to gravity?

Near the surface of the Earth, g ≈ 9.8 m/s² (the standard value is 9.80665 m/s²), directed toward the center of the Earth. This means that the downward velocity of a falling object increases by about 9.8 m/s every second. The value is the same for all masses, because the gravitational force is proportional to the mass, and the acceleration is force divided by mass, so the mass cancels. The value varies a little: about 9.78 m/s² at the equator and 9.83 m/s² at the poles, and it decreases with altitude. For quick calculations, 10 m/s² is sometimes used.

How are the equations applied?

Choose a positive direction (for example, up) and set a = −g. Then:

• v = u − gt
• h = ut − ½gt²
• v² = u² − 2gh

For an object dropped from rest, u = 0, so it falls a distance h = ½gt² in time t, and reaches v = gt. For an object thrown upward with speed u, at the highest point v = 0, so the time to the top is u ÷ g and the maximum height is u² ÷ 2g. The motion is symmetrical (without air resistance): the time up equals the time down, and the object returns to the starting height with the same speed that it was thrown with.

Values of g compared

Worked example: dropped and thrown objects

1. Dropped from a height. A stone is dropped from a 45 m cliff. Use g = 9.8 m/s².
   • h = ½gt², so t = √(2h ÷ g) = √(90 ÷ 9.8) = √9.18 = 3.0 s.
   • Speed on impact: v = gt = 9.8 × 3.03 = 29.7 m/s, or about 30 m/s. Check: v = √(2gh) = √(2 × 9.8 × 45) = √882 = 29.7 m/s.
2. Thrown upward. A ball is thrown vertically upward at 20 m/s.
   • Time to the top: t = u ÷ g = 20 ÷ 9.8 = 2.04 s.
   • Maximum height: h = u² ÷ 2g = 400 ÷ 19.6 = 20.4 m.
   • Total flight time back to the hand: 2 × 2.04 = 4.08 s. The velocity on return is −20 m/s (20 m/s downward).

How was free fall studied?

Aristotle taught that heavier bodies fall faster. Galileo disproved this in the late 1500s and early 1600s, using inclined planes to slow the motion so that it could be measured (the story of the Leaning Tower of Pisa experiment is probably a legend). Newton explained in 1687 that gravity gives all bodies the same acceleration, and in 1971 the Apollo 15 hammer-and-feather demonstration confirmed it on the Moon.

Which mistakes are common?

Mistake 1: Believing that heavy objects fall faster

Without air resistance, all objects have the same acceleration.

Mistake 2: Saying that the acceleration is zero at the top

The velocity is zero at the top, but the acceleration is still g downward.

Mistake 3: Mixing signs

If up is positive, use −9.8 m/s² for g in all stages of the flight.

Mistake 4: Confusing g with G

g is the local acceleration due to gravity, and G is the universal gravitational constant.