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"Accelerate" redirects here. For other uses, see Accelerate (disambiguation).
This article is about physics term. For the R.E.M. album, see Accelerate (R.E.M. album). REM is an American rock band formed in Athens, Georgia, in 1980 by Michael Stipe ( lead vocals) Peter Buck ( Guitar Accelerate is the fourteenth studio album by the American Alternative rock band R
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). In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change In Physics, velocity is defined as the rate of change of Position. In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change It is then a vector quantity with dimension length/time². Length is the long Dimension of any object The length of a thing is the distance between its ends its linear extent as measured from end to end For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of 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. Newton's laws of motion are three Physical laws which provide relationships between the Forces acting on a body and the motion of the

Contents

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. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Proper acceleration is the physical acceleration experienced by an object This was the basis for his development of general relativity, a relativistic theory of gravity. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Gravitation is a natural Phenomenon by which objects with Mass attract one another 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. In physics the twin paradox is a thought experiment in Special Relativity, in which a person who makes a journey into space in a high-speed rocket will return home to find he 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). General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 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. In Physics, an inertial frame of reference is a Frame of reference which belongs to a set of frames in which Physical laws hold in the same and simplest (The path from these considerations to the full theory of general relativity is traced in the Introduction to general relativity. General relativity (GR is a Theory of Gravitation that was developed by Albert Einstein between 1907 and 1915 )

Formula

The formula for the average acceleration over a time period Δt is

\mathbf{\bar{a}}=\frac{\mathbf{v}(t+\Delta t)-\mathbf{v}(t)}{\Delta t}

where

\mathbf{v}(t+\Delta t) is the final velocity
\mathbf{v}(t) is the initial velocity
\mathbf{t} is the initial time and \Delta \mathbf{t} is the change in time

The formula for the instantaneous acceleration at time t is

\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}

Thus acceleration is the first derivative of velocity. In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change 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. In Mathematics, the concept of a " limit " is used to describe the Behavior of a function as its argument either "gets close" 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{\mathbf{a}}\int_{t_0}^{t_1}\mathrm{d}t=\int_{t_0}^{t_1}\mathbf{a}(t)\mathrm{d}t

Putting it all together means:

\mathbf{a} = \frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t} = \frac{\mathrm{d}^2\mathbf{r}}{\mathrm{d}t^2}

where

\mathbf{a} is acceleration
\mathbf{v} is velocity
\mathbf{r} is position
t is time

See also

External links

Kinematics

← Integrate . In Calculus, the mean value theorem states roughly that given a section of a smooth curve there is at least one point on that section at which the Derivative Uniform, or constant, acceleration is a type of motion in which the Velocity of an object changes equal amounts in equal time periods Angular acceleration is the rate of change of Angular velocity over Time. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Kinematics ( Greek κινειν, kinein, to move is a branch of Classical mechanics which describes the motion of objects without Proper acceleration is the physical acceleration experienced by an object Kinematics ( Greek κινειν, kinein, to move is a branch of Classical mechanics which describes the motion of objects without The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space . . Differentiate →
Displacement (Distance) | Velocity (Speed) | Acceleration | Jerk | Snap
In Calculus, a branch of mathematics the derivative is a measurement of how a function changes when the values of its inputs change In Physics, displacement is the vector that specifies the position of a point or a particle in reference to a previous position or to the origin of the chosen Distance is a numerical description of how far apart objects are In Physics, velocity is defined as the rate of change of Position. Speed is the rate of motion, or equivalently the rate of change in position often expressed as Distance d traveled per unit of In Physics, jerk, jolt (especially in British English) surge or lurch, is the rate of change of Acceleration; that is

Dictionary

acceleration

-noun

  1. (uncountable) The act of accelerating, or the state of being accelerated; increase of motion or action; as opposed to retardation or deceleration.
  2. (countable) The amount by which a speed or velocity increases (and so a scalar quantity or a vector quantity).
  3. (physics) The change of velocity with respect to time (can include deceleration or changing direction).
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