Aceleration

Aceleration (often misspelled as acceleration) refers to the rate at which an object's velocity changes over time. It is a vector quantity with both magnitude and direction, and its SI unit is meters per second squared (m/s^2).

Mathematically, acceleration a is the time derivative of velocity v: a = dv/dt. For motion with constant acceleration, velocity evolves as v = u + a t, where u is the initial velocity, and position evolves as s = u t + 1/2 a t^2.

Common types include linear acceleration (along a straight path) and angular acceleration in rotation, where angular acceleration alpha is the time rate of change of angular velocity. In circular motion, centripetal acceleration a_c = v^2/r points toward the center; tangential acceleration a_t = dv/dt reflects changing speed.

Gravity on Earth provides approximately g = 9.81 m/s^2 of downward acceleration, but this is a coordinate acceleration depending on the frame; actual measurement by an accelerometer gives proper acceleration, the physical acceleration felt by a device.

Measurement and applications: accelerometers detect acceleration and are used in smartphones, vehicles, and spacecraft. Acceleration concepts are central to kinematics, dynamics, and orbital mechanics; engineering and sports rely on accelerations to analyze motion.