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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.

Contents [hide]

1 Explanation

2 Relation to relativity

3 References

4 External links and references

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Explanation

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

equation

where

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:

where

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.

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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.