Equations for a falling body

Equations for a falling body relate vertical displacement, velocity, acceleration, and time under gravity. In the ideal model, air resistance is neglected and acceleration is constant.

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Constant-acceleration equations: Kinematic equations relating displacement, velocity, acceleration, and time when acceleration is constant. They provide the general framework from which the falling-body equations follow.
One-dimensional motion: Motion restricted to a single spatial axis, described by one position coordinate. A falling body's vertical motion can be treated along one axis.
Projectile motion: Two-dimensional motion under gravity, often modeled with constant horizontal velocity and vertical acceleration. Its vertical component follows the same equations as a falling body.
Linear drag: A resistive force proportional to an object's velocity through a fluid. It changes falling motion from constant acceleration toward a finite terminal speed.
Gravitational acceleration: The acceleration produced by gravity; near Earth's surface its magnitude is about 9.8 meters per second squared. It supplies the constant acceleration used in the ideal equations.
Coordinate system: A framework of axes and an origin used to assign positions and directions. Choosing the vertical axis sets the signs of displacement, velocity, and gravity.
Reaction time: The interval between a stimulus and a person's response to it. Drop tests use falling distance to estimate how long a person takes to react.
Quadratic drag: A fluid resistance force approximately proportional to the square of an object's speed. It is often a better model than constant acceleration for fast falls through air.
Free fall: Motion in which gravity is the only force acting on an object. The equations model this motion when air resistance is ignored.
Scalar and vector quantities: Scalars have magnitude alone, while vectors have magnitude and direction. Velocity and displacement carry direction, so their signs matter in the equations.