# Dictionary Definition

accelerating adj : increasing in speed; becoming progressively faster; "the accelerating inflation was cause for great concern"

# User Contributed Dictionary

## English

### Verb

accelerating
1. present participle of accelerate

# Extensive Definition

In physics, acceleration is defined as the rate of change of velocity, or as the second derivative of position (with respect to time). It is then a vector quantity with dimension length/time². In SI units, acceleration is measured in meters/second² (m·s-2). The term "acceleration" generally refers to the rate of change in instantaneous velocity. (velocity is speed and direction)
In common speech, the term acceleration is only used for an increase in speed; a decrease in speed is called deceleration. In physics, any increase or decrease in speed is referred to as acceleration and similarly, motion in a circle at constant speed is also an acceleration, since the direction component of the velocity is changing. See also Newton's Laws of Motion.

## Relation to relativity

After completing his theory of special relativity, Albert Einstein realized that forces felt by objects undergoing constant proper acceleration are indistinguishable from those in a gravitational field. This was the basis for his development of general relativity, a relativistic theory of gravity. This is also the basis for the popular Twin paradox, which asks why one twin ages less when moving away from his sibling at near light-speed and then returning, since the non-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. (The path from these considerations to the full theory of general relativity is traced in the Introduction to general relativity.)

## Formula

The formula for the average acceleration over a time period \Delta t is
\mathbf=\frac
where
\mathbf(t+\Delta t) is the final velocity
\mathbf(t) is the initial velocity
\mathbf is the initial time and \Delta \mathbf is the change in time
The formula for the instantaneous acceleration at time t is
\mathbf(t)=\lim_\frac=\frac
Thus acceleration is the first derivative of velocity. One should note that the expression (Final position - Initial Position) / (Total time taken) is the average velocity, and the limit as the time interval approaches zero is the instantaneous velocity. Therefore, velocity is the first derivative of position, making acceleration the second.
One should also note that the average and instantaneous accelerations over a time period \Delta t=t_1-t_0 are related through the Mean Value Theorem for Integrals:
\bar\int_^\mathrmt=\int_^\mathbf(t)\mathrmt
Putting it all together means:
\mathbf = \frac = \frac
where
\mathbf is acceleration
\mathbf is velocity
\mathbf is position
is time
accelerating in Afrikaans: Versnelling
accelerating in Arabic: تسارع
accelerating in Asturian: Aceleración
accelerating in Bengali: ত্বরণ
accelerating in Min Nan: Ka-sok-tō͘
accelerating in Belarusian: Паскарэнне
accelerating in Bosnian: Ubrzanje
accelerating in Bulgarian: Ускорение
accelerating in Catalan: Acceleració
accelerating in Czech: Zrychlení
accelerating in Danish: Acceleration
accelerating in German: Beschleunigung
accelerating in Estonian: Kiirendus
accelerating in Modern Greek (1453-): Επιτάχυνση
accelerating in Spanish: Aceleración
accelerating in Esperanto: Akcelo
accelerating in Basque: Azelerazio
accelerating in Persian: شتاب
accelerating in French: Accélération
accelerating in Irish: Luasghéarú
accelerating in Manx: Bieauaghey
accelerating in Galician: Aceleración
accelerating in Hakka Chinese: Kâ-suk-thu
accelerating in Korean: 가속도
accelerating in Croatian: Ubrzanje
accelerating in Ido: Acelero
accelerating in Indonesian: Percepatan
accelerating in Icelandic: Hröðun
accelerating in Italian: Accelerazione
accelerating in Hebrew: תאוצה
accelerating in Latin: Acceleratio
accelerating in Latvian: Paātrinājums
accelerating in Lithuanian: Pagreitis
accelerating in Hungarian: Gyorsulás
accelerating in Malayalam: ത്വരണം
accelerating in Malay (macrolanguage): Pecutan
accelerating in Mongolian: Хурдатгал
accelerating in Dutch: Versnelling (natuurkunde)
accelerating in Japanese: 加速度
accelerating in Norwegian: Akselerasjon
accelerating in Norwegian Nynorsk: Akselerasjon
accelerating in Novial: Akseleratione
accelerating in Polish: Przyspieszenie
accelerating in Portuguese: Aceleração
accelerating in Quechua: P'ikwachiy
accelerating in Russian: Ускорение
accelerating in Sicilian: Accilirazzioni
accelerating in Simple English: Acceleration
accelerating in Slovak: Zrýchlenie
accelerating in Slovenian: Pospešek
accelerating in Serbian: Убрзање
accelerating in Serbo-Croatian: Ubrzanje
accelerating in Finnish: Kiihtyvyys
accelerating in Swedish: Acceleration
accelerating in Telugu: త్వరణము
accelerating in Thai: ความเร่ง
accelerating in Vietnamese: Gia tốc
accelerating in Turkish: İvme
accelerating in Ukrainian: Прискорення
accelerating in Chinese: 加速度