Acceleration 2443 225212953 2008-07-12T14:19:11Z Brews ohare 5680311 link; capitalization {{redirect|Accelerate}} [[Image:Acceleration.svg|255px|thumb|Acceleration is the rate of change of velocity. At any point on a speed-time graph, the magnitude of the acceleration is given by the gradient of the tangent to the curve at that point.]] In physics, '''acceleration''' is defined as the [[Derivative|rate of change]] of [[velocity]], or as the second [[derivative]] of position (with respect to time). It is then a [[vector (spatial)|vector]] quantity with dimension [[length]]/[[time]]². In [[SI|SI units]], acceleration is measured in [[Metre per second squared|meters/second²]] (m·s<sup>-2</sup>). 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]] and [[centripetal force]]. ==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 frame of reference|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 <math>\Delta t</math> is :<math>\mathbf{\bar{a}}=\frac{\mathbf{v}(t+\Delta t)-\mathbf{v}(t)}{\Delta t}</math> where :<math>\mathbf{v}(t+\Delta t)</math> is the final velocity :<math>\mathbf{v}(t)</math> is the initial velocity :<math>\mathbf{t}</math> is the initial time and <math>\Delta \mathbf{t}</math> is the change in time The formula for the instantaneous acceleration at time <math>t</math> is :<math>\mathbf{a}(t)=\lim_{\Delta t \to 0}\frac{\mathbf{v}(t+\Delta t)-\mathbf{v}(t)}{\Delta t}=\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t}</math> 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 (mathematics)|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 <math>\Delta t=t_1-t_0</math> are related through the [[Mean value theorem| mean value theorem for integrals]]: :<math>\bar{\mathbf{a}}\int_{t_0}^{t_1}\mathrm{d}t=\int_{t_0}^{t_1}\mathbf{a}(t)\mathrm{d}t</math> Putting it all together means: :<math>\mathbf{a} = \frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t} = \frac{\mathrm{d}^2\mathbf{r}}{\mathrm{d}t^2}</math> where :<math>\mathbf{a}</math> is '''acceleration''' :<math>\mathbf{v}</math> is '''velocity''' :<math>\mathbf{r}</math> is '''position''' :<math>{t}</math> is '''time''' ==See also== * [[Uniform Acceleration]] * [[Angular acceleration]] * [[General relativity#Coordinate vs. physical acceleration|Coordinate vs. physical acceleration]] * [[Derivatives of position]] * [[Equations of Motion]] * [[Proper acceleration|Proper Acceleration]] * [[0 to 60 mph]] ==External links== * [http://www.lightandmatter.com/html_books/1np/ch03/ch03.html Acceleration and Free Fall] - a chapter from an online textbook *[http://physnet.org/home/modules/pdf_modules/m72.pdf ''Trajectories and Radius, Velocity, Acceleration''] on [http://www.physnet.org Project PHYSNET] (ERROR - PAGE MOVED) * [http://www.scienceaid.co.uk/physics/forces/motion.html Science aid: Movement] * [http://eroosevelths.pgcps.org/~pruszko/Vectors.pdf The physics classroom ] * [http://science.dirbix.com/physics/acceleration Science.dirbix: Acceleration] * [http://www.ajdesigner.com/constantacceleration/cavelocitya.php Acceleration Calculator] * [http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l1b.html Motion Characteristics for Circular Motion] {{Kinematics}} [[Category:Physical quantity]] [[Category:Dynamics]] [[zh-yue:加速度]] [[af:Versnelling]] [[ar:تسارع]] [[ast:Aceleración]] [[bn:ত্বরণ]] [[zh-min-nan:Ka-sok-tō͘]] [[be:Паскарэнне]] [[be-x-old:Паскарэньне]] [[bs:Ubrzanje]] [[bg:Ускорение]] [[ca:Acceleració]] [[cs:Zrychlení]] [[cy:Cyflymiad]] [[da:Acceleration]] [[de:Beschleunigung]] [[et:Kiirendus]] [[el:Επιτάχυνση]] [[es:Aceleración]] [[eo:Akcelo]] [[eu:Azelerazio]] [[fa:شتاب]] [[fr:Accélération]] [[ga:Luasghéarú]] [[gv:Bieauaghey]] [[gl:Aceleración]] [[hak:Kâ-suk-thu]] [[ko:가속도]] [[hr:Ubrzanje]] [[io:Acelero]] [[id:Percepatan]] [[is:Hröðun]] [[it:Accelerazione]] [[he:תאוצה]] [[la:Acceleratio]] [[lv:Paātrinājums]] [[lt:Pagreitis]] [[hu:Gyorsulás]] [[ml:ത്വരണം]] [[ms:Pecutan]] [[mn:Хурдатгал]] [[nl:Versnelling (natuurkunde)]] [[ja:加速度]] [[no:Akselerasjon]] [[nn:Akselerasjon]] [[nov:Akseleratione]] [[pl:Przyspieszenie]] [[pt:Aceleração]] [[qu:P'ikwachiy]] [[ru:Ускорение]] [[scn:Accilirazzioni]] [[simple:Acceleration]] [[sk:Zrýchlenie]] [[sl:Pospešek]] [[sr:Убрзање]] [[sh:Ubrzanje]] [[fi:Kiihtyvyys]] [[sv:Acceleration]] [[te:త్వరణము]] [[th:ความเร่ง]] [[vi:Gia tốc]] [[tr:İvme]] [[uk:Прискорення]] [[zh:加速度]]