acceleration

Acceleration is the second step in the chain of derivatives that describes motion. If position tells you where something is, and velocity tells you how that position is changing, then acceleration tells you how the velocity itself is changing. Mathematically, a = dv/dt = d²x/dt².

The most familiar example is free fall near the Earth's surface, where every object — in the absence of air resistance — accelerates downward at approximately 9.81 m/s² regardless of mass. This constant is called g, and it defines the local strength of gravity. It is the reason a feather and a hammer, dropped together in a vacuum, land at the same moment. Galileo suspected this; the Apollo 15 astronaut David Scott proved it live on the Moon in 1971.

In one dimension, acceleration is a signed number: positive means speeding up in the direction of motion, negative means slowing down (deceleration is just negative acceleration along the direction of travel). In higher dimensions, acceleration is a vector that can change either the magnitude or the direction of velocity — or both. A car rounding a curve at constant speed is still accelerating, because its velocity vector is rotating.

The SI unit is metres per second squared (m/s²), which reads as 'metres per second, per second' — the change in velocity (metres per second) per unit of time (per second). Newton's second law, F = ma, ties acceleration directly to force: the amount of push needed to change an object's motion is proportional to the acceleration you want to produce.