In physics, acceleration is defined as the rate of change (or time derivative) of velocity. It is thus a vector quantity with dimension length/time^{2}. In SI units this is meter/second^{2}.
To accelerate an object is to change its velocity over a period of time. Note that in this strict scientific sense, the definition of acceleration includes both positive and negative acceleration  called acceleration and deceleration in common speech, respectively  as well as change of direction. Acceleration is defined technically as "the rate of change of velocity of an object with respect to time" and is given by the equation
One common unit of acceleration is g, one g being the acceleration caused by the gravity of Earth at sea level on the equator (~9.81 m/s^{2})
In classical mechanics, acceleration a is related to force F and mass m by way of Newton's second law:
(assuming that the mass is constant).
As a result of its invariance under the Galilean transformations, acceleration is an absolute quantity in classical mechanics.
After defining his theory of Special Relativity, Einstein realized that forces felt by objects undergoing constant acceleration are indistinguishable from those in a gravitational field, and thus defined General Relativity (which also resolved how gravity's effects could be limited by the speed of light, but that is another story).
A key point of General Relativity is that it solved the "why does only one object feel accelerated?" problem which had plagued philosophers and scientists since Newton's time (and caused Newton to endorse absolute space). Simply put, if you hop in your car and accelerate away from your friend, you could say (given your frame of reference) that it is your friend who is accelerating away from you, although only you feel any force. This is also the basis for the popular Twin's Paradox, which asks why only one twin ages when moving away from his sibling at near lightspeed and then returning, since the aging twin can say that it is the other twin that was moving.
In special relativity, only inertial frames (nonaccelerated frames) can be used and are equivalent; general relativity considers all frames, even accelerated ones, to be equivalent. With changing velocity, accelerated objects exist in warped space (as do those that reside in a gravitational field). Therefore, frames of reference must include a description of their local spacetime curvature to qualify as complete.
The rate of change of acceleration is known as jerk or yank.
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