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Acceleration

In physics, acceleration is defined as the rate of change (or time
derivative) of velocity. It is thus a vector quantity with dimension
length/time². In SI units this is meter/second².

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 (or retardation) 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

[a = {\mathbf{d}v \over \mathbf{d}t}]

where a is the acceleration vector, v is the velocity vector expressed in
m/s, and t is time expressed in seconds. This equation gives a the units of
m/s/s, or m/s² (read as "meters per second per second", or "meters per
second squared").

An alternative equation is:

[a = {v - u \over t}]

where a is acceleration (m/s²), u is initial velocity (m/s), v is final
velocity (m/s), and t is time (s).

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/s²)

In classical mechanics, acceleration a is related to force F and mass m by
way of Newton's second law:

F = m a

(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, Albert 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 paradox, which asks why only one twin
ages when moving away from his sibling at near light-speed and then
returning, since the aging twin can say that it is the other twin that was
moving.

In special relativity, only inertial frames (non-accelerated 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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