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16-September-2008 16:15:13 - Acceleration Accelerate redirects here. For other uses, see Accelerate disambiguation. 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. 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 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 and centripetal force. Contents 1 Relation to relativity 2 Formula 3 See also 4 External links 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 Δt is \mathbf\bara=\frac\mathbfvt+\Delta t-\mathbfvt\Delta t where \mathbfvt+\Delta t is the final velocity \mathbfvt is the initial velocity \mathbft is the initial time and \Delta \mathbft is the change in time The formula for the instantaneous acceleration at time t is \mathbfat=\lim_\Delta t \to 0\frac\mathbfvt+\Delta t-\mathbfvt\Delta t=\frac\mathrmd\mathbfv\mathrmdt 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 Δt = t1 - t0 are related through the mean value theorem for integrals: \bar\mathbfa\int_t_0^t_1\mathrmdt=\int_t_0^t_1\mathbfat\mathrmdt Putting it all together means: \mathbfa = \frac\mathrmd\mathbfv\mathrmdt = \frac\mathrmd^2\mathbfr\mathrmdt^2 where \mathbfa is acceleration \mathbfv is velocity \mathbfr is position t is time In relation to Newton's law of Force, F = ma, acceleration is equal to the net force acting on the object divided by the object's mass: a = \fracFm See also Uniform acceleration Angular acceleration Coordinate vs. physical acceleration Derivatives of position Equations of Motion Proper Acceleration 0 to 60 mph Shock mechanics External links Acceleration and Free Fall - a chapter from an online textbook Trajectories and Radius, Velocity, Acceleration on Project PHYSNET ERROR - PAGE MOVED Science aid: Movement The physics classroom Science.dirbix: Acceleration Acceleration Calculator Motion Characteristics for Circular Motion Practical Guide to Accelerometers Kinematics â†? Integrate ... Differentiate → Displacement Distance | Velocity Speed | Acceleration | Jerk | Snap Retrieved from http://en..org/wiki/Acceleration Categories: Physical quantities | Dynamics Views Article Discussion this page History Personal tools Log in / create account Navigation Main page Contents Featured content Current events Random article Search Go Search Interaction Community portal Recent changes Contact Donate to Help Toolbox What links here Related changes Upload file Special pages Printable version Permanent link Cite this page Languages Afrikaans العربية Asturianu Bân-lâm-gú БеларуÑ?каÑ? БеларуÑ?каÑ? тарашкевіца Bosanski БългарÑ?ки Català Česky Cymraeg Dansk Deutsch Eesti Ελληνικά Español Esperanto Euskara Ù?ارسی Français Gaeilge Gaelg Galego Hak-kâ-fa í•œêµì–´ Hrvatski Ido Bahasa Indonesia Ã?slenska Italiano עברית ქáƒ?რთული Latina LatvieÅ¡u Lietuvių Magyar മലയാളം Bahasa Melayu Монгол Nederlands ‪Norsk bokmÃ¥l‬ ‪Norsk nynorsk‬ Novial Polski Português Runa Simi Română РуÑ?Ñ?кий Sicilianu Simple English SlovenÄ?ina SlovenÅ¡Ä?ina СрпÑ?ки / Srpski Srpskohrvatski / СрпÑ?кохрватÑ?ки Basa Sunda Suomi Svenska తెలà±?à°—à±? ไทย Tiếng Việt Türkçe УкраїнÑ?ька 粵語 ä¸æ–‡ This page was last modified on 9 August 2008, at 01:14
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