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Acceleration is the time rate of change of velocity, and at any point
on a v-t graph, it is given by the gradient of the tangent to that
pointIn physics, acceleration (symbol: a) 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.
2 Relation to relativity
4 External links and references
To accelerate an object is to change its velocity over a period of
time. In this strict scientific sense, acceleration can have positive
and negative values respectively called acceleration and
deceleration (or retardation) in common speech 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
a is the acceleration vector
v is the velocity vector expressed in m/s
t is time expressed in seconds.
This equation gives a the units of m/(s·s), or m/s² (read as "metres
per second per second", or "metres per second squared").
An alternative equation is:
â is the average acceleration (m/s²)
u is the initial velocity (m/s)
v is the final velocity (m/s)
t is the time interval (s)
Transverse acceleration (perpendicular to velocity) causes change in
direction. If it is constant in magnitude and changing in direction
with the velocity, we get a circular motion. For this centripetal
acceleration we have
One common unit of acceleration is g, one g being the acceleration
caused by the gravity of Earth at sea level at 45° latitude (Paris),
or about 9.81 m/s².
Accelerating acceleration or jerk is the rate of change of an
object's acceleration over time.
In classical mechanics, acceleration is related to force and mass
(assumed to be constant) by way of Newton's second law:
As a result of its invariance under the Galilean transformations,
acceleration is an absolute quantity in classical mechanics.
Relation to relativity
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 that also explained how gravity's effects
could be limited by the speed of light.
If you 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. General relativity 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). In
special relativity, only inertial frames of reference (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.
Acceleration can be measured using an accelerometer.