An object follows free-fall motion when gravity dominates its motion and effects such as air resistance can be neglected. Near Earth's surface, over distances small compared with Earth's radius, the gravitational acceleration is approximately constant and directed downward.

Its magnitude is denoted by

$$g\approx 9.81,\mathrm{m/s^2}.$$

If upward is chosen as the positive direction, the acceleration is

$$a=-g.$$

This approximation is remarkably useful: all objects at the same location have approximately the same free-fall acceleration when drag and other nongravitational effects are negligible. The different fall of a feather and a compact ball in ordinary air is mainly a drag effect, not a different value of gravitational acceleration.

Free fall does not mean moving downward

The acceleration is downward regardless of the instantaneous direction of motion. A ball thrown upward is already following free-fall motion after release. While it rises, its velocity points upward but its acceleration points downward. At the highest point its instantaneous velocity is zero, yet its acceleration remains

$$a=-g.$$

The ball then accelerates downward.

Constant-acceleration equations

Because $g$ is approximately constant in this model, the constant-acceleration relations apply directly. With initial height $y_0$ and vertical velocity $v_0$,

$$v=v_0-gt,$$

and

$$y=y_0+v_0t-\frac12gt^2.$$

The signs follow from the chosen coordinate direction; the formulas do not require the object itself to keep moving in one direction.

Worked example: a ball thrown upward

A ball is released from $y_0=0$ with

$$v_0=10,\mathrm{m/s}.$$

At the highest point $v=0$, so

$$0=10-(9.81)t,$$

which gives

$$t\approx1.02,\mathrm s.$$

Its height then is

$$y=(10)(1.02)-\frac12(9.81)(1.02)^2\approx5.1,\mathrm m.$$

The ball obeys the same downward acceleration on both the upward and downward portions of its trajectory.

Free fall therefore describes a motion model: near Earth's surface and with nongravitational effects negligible, the acceleration is approximately constant and downward. It does not mean that the object must already be moving downward, nor does it mean that gravity is absent.