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ac·cel·er·a·tion

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(ăk-sĕl'ə-rā'shən) pronunciation
n.
    1. The act of accelerating.
    2. The process of being accelerated.
  2. (Abbr. a) Physics. The rate of change of velocity with respect to time.

acceleration

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Britannica Concise Encyclopedia:

acceleration

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Rate of change of velocity. Acceleration, like velocity, is a vector quantity: it has both magnitude and direction. The velocity of an object moving on a straight path can change in magnitude only, so its acceleration is the rate of change of its speed. On a curved path, the velocity may or may not change in magnitude, but it will always change in direction, which means that the acceleration of an object moving on a curved path can never be zero. If velocity is stated in metres per second (m/s) and the time interval in seconds (s), then the units of acceleration are metres per second per second (m/s/s, or m/s2). centripetal acceleration.

For more information on acceleration, visit Britannica.com.

McGraw-Hill Science & Technology Encyclopedia:

Acceleration

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The time rate of change of velocity. Since velocity is a directed or vector quantity involving both magnitude and direction, a velocity may change by a change of magnitude (speed) or by a change of direction or both. It follows that acceleration is also a directed, or vector, quantity. If the magnitude of the velocity of a body changes from v1 ft/s to v2 ft/s in t seconds, then the average acceleration a has a magnitude given by Eq. (1):
1. a = \frac{\rm velocity\,\, change}{\rm elapsed\,\, time} = \frac{v_2 - v_1}{t_2 - t_1} = \frac{\Delta v}{\Delta t}
To designate it fully the direction should be given, as well as the magnitude. See also Velocity.

Instantaneous acceleration is defined as the limit of the ratio of the velocity change to the elapsed time as the time interval approaches zero. When the acceleration is constant, the average acceleration and the instantaneous acceleration are equal.

Whenever a body is acted upon by an unbalanced force, it will undergo acceleration. If it is moving in a constant direction, the acting force will produce a continuous change in speed. If it is moving with a constant speed, the acting force will produce an acceleration consisting of a continuous change of direction. In the general case, the acting force may produce both a change of speed and a change of direction.

Angular acceleration is a vector quantity representing the rate of change of angular velocity of a body experiencing rotational motion. If, for example, at an instant t1, a rigid body is rotating about an axis with an angular velocity ω1, and at a later time t2, it has an angular velocity ω2, the average angular acceleration α is given by Eq. (2), in radians per second per second.
2. \overline{\alpha} = \frac{\omega_{2} - \omega_{1}}{t_2 - t_1} = \frac{\Delta \omega}{\Delta t}
The instantaneous angular acceleration is given by α = dω/dt.

When a body moves in a circular path with constant linear speed at each point in its path, it is also being constantly accelerated toward the center of the circle under the action of the force required to constrain it to move in its circular path. This acceleration toward the center of path is called radial acceleration. The component of linear acceleration tangent to the path of a particle subject to an angular acceleration about the axis of rotation is called tangential acceleration. See also Rotational motion.

Barron's Business Dictionary:

acceleration

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In real estate law: (1) hastening of the time for enjoyment of a remainder interest due to the premature termination of a preceding estate; and (2) process by which, under the terms of a mortgage or similar obligation, an entire debt is to be regarded as due upon the borrower’s failure to pay a single installment or to fulfill some other duty.
See also acceleration clause.

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Antonyms by Answers.com:

acceleration

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n

Definition: increasing speed, timing
Antonyms: deceleration, deferral, hindrance, retardation, slowing down

McGraw-Hill Dictionary of Architecture & Construction:

acceleration

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1. The rate of change of the velocity of a moving body.
2. The rate of change, esp. the quickening of the natural progress of a process, such as hardening, setting, or strength development of concrete.

Oxford Dictionary of Sports Science & Medicine:

acceleration

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The rate of change in velocity or the change in velocity occurring over a given time interval: acceleration = change of velocity/time. It is usually expressed as metres per second squared (ms−2). When an object speeds up, slows down, starts, stops, or changes direction, it is accele rating. Acceleration can be positive or negative. See also acceleration, law of.

Columbia Encyclopedia:

acceleration

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acceleration, change in the velocity of a body with respect to time. Since velocity is a vector quantity, involving both magnitude and direction, acceleration is also a vector. In order to produce an acceleration, a force must be applied to the body. The magnitude of the force F must be directly proportional to both the mass of the body m and the desired acceleration a, according to Newton's second law of motion, F=ma. The exact nature of the acceleration produced depends on the relative directions of the original velocity and the force. A force acting in the same direction as the velocity changes only the speed of the body. An appropriate force acting always at right angles to the velocity changes the direction of the velocity but not the speed. An example of such an accelerating force is the gravitational force exerted by a planet on a satellite moving in a circular orbit. A force may also act in the opposite direction from the original velocity. In this case the speed of the body is decreased. Such an acceleration is often referred to as a deceleration. If the acceleration is constant, as for a body falling near the earth, the following formulas may be used to compute the acceleration a of a body from knowledge of the elapsed time t, the distance s through which the body moves in that time, the initial velocity vi, and the final velocity vf:
a=(vf2−vi2)/2sa=2(s−vit)/t2a=(vf−vi)/t

West's Encyclopedia of American Law:

Acceleration

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This entry contains information applicable to United States law only.

A hastening; a shortening of the time until some event takes place.

A person who has the right to take possession of property at some future time may have that right accelerated if the present holder loses his or her legal right to the property. If a life estate fails for any reason, the remainder is accelerated.

The principle of acceleration can be applied when it becomes clear that one party to a contract is not going to perform his or her obligations. Anticipatory repudiation, or the possibility of future breach, makes it possible to move the right to remedies back to the time of repudiation rather than to wait for the time when performance would be due and an actual breach would occur.

Oxford Companion to the Mind:

acceleration

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Acceleration of the body is sensed in the inner ear by the otoliths, small weights of calcium carbonate suspended on stalks. Accelerated movements of the head produce deflections of the stalks, since the otoliths do not respond immediately to movement because of their inertia. Unaccelerated motion cannot be sensed intrinsically by any sense or by any physical instrument, but only by reference to external objects that may themselves be moving. So there is ambiguity, such as occurs when a stationary train appears, to one who is in it, to move when a neighbouring train moves past it. Here the visual sense of movement dominates the sensing of acceleration — or rather the lack of acceleration — for the observer in the stationary train.

(Published 1987)
Dictionary of Cultural Literacy: Science:

acceleration

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A change in the velocity of an object.

  • The most familiar kind of acceleration is a change in the speed of an object. An object that stays at the same speed but changes direction, however, is also being accelerated. (See force.)

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    categories related to 'acceleration'

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    Wikipedia on Answers.com:

    Acceleration

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    "Accelerate" redirects here. For other uses, see Accelerate (disambiguation).
    Classical mechanics
    History of classical mechanics · Timeline of classical mechanics
    Fundamental concepts
    Space · Time · Velocity · Speed · Mass · Acceleration · Gravity · Force · Impulse · Torque / Moment / Couple · Momentum · Angular momentum · Inertia · Moment of inertia · Reference frame · Energy · Kinetic energy · Potential energy · Mechanical work · Virtual work · D'Alembert's principle

    In physics, acceleration is the rate of change of velocity with time.[1] In one dimension, acceleration is the rate at which something speeds up or slows down. For example, a car driving away (from standstill) is increasing its speed and is thus accelerating. Similarly, a car braking to stop in front of a traffic light is still said (in physics) to undergo acceleration, although now a negative one. In common speech, it is said to be decelerating.

    However, velocity has both a magnitude and direction (i.e. it is a vector), and thus acceleration is also a vector. As such, it describes the rate of change of both the magnitude (the speed) and the direction of velocity.[2][3] This means that an object moving in a circular motion—such as a satellite orbiting the earth—is also accelerating, even though it may be moving at a constant speed. When an object is executing such a motion where it changes direction, but not speed, it is said to be undergoing centripetal (directed towards the center) acceleration. Oppositely, a change in the speed of an object, but not its direction of motion, is a tangential acceleration.

    Acceleration has the dimensions L T −2. In SI units, acceleration is measured in meters per second squared (m/s2).

    Proper acceleration, the acceleration of a body relative to a free-fall condition, is measured by an instrument called an accelerometer.

    In classical mechanics, for a body with constant mass, the acceleration of the body is proportional to the net force acting on it (Newton's second law):

    \mathbf{F} = m\mathbf{a} \quad \to \quad \mathbf{a} = \mathbf{F}/m

    where F is the resultant force acting on the body, m is the mass of the body, and a is its acceleration.

    Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time t is found in the limit as time interval Δt → 0.
    Components of acceleration for a planar curved motion. The tangential component at is due to the change in speed of traversal, and points along the curve in the direction of the velocity vector. The centripetal component ac is due to the change in direction of the velocity vector and is normal to the trajectory, pointing toward the center of curvature of the path.

    Average acceleration is the change in velocity (Δv) divided by the change in time (Δt). Instantaneous acceleration is the acceleration at a specific point in time which is for a very short interval of time as Δt approaches zero. Acceleration can therefore be computed as the derivative (with respect to time) of velocity.

    Contents

    Tangential and centripetal acceleration

    See also: Local coordinates

    The velocity of a particle moving on a curved path as a function of time can be written as:

    \mathbf{v} (t) =v(t) \frac {\mathbf{v}(t)}{v(t)} = v(t) \mathbf{u}_\mathrm{t}(t) ,

    with v(t) equal to the speed of travel along the path, and

    \mathbf{u}_\mathrm{t} = \frac {\mathbf{v}(t)}{v(t)} \ ,

    a unit vector tangent to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speed v(t) and the changing direction of ut, the acceleration of a particle moving on a curved path on a planar surface can be written using the chain rule of differentiation[4] and the derivative of the product of two functions of time as:

    \begin{alignat}{3} \mathbf{a} & = \frac{d \mathbf{v}}{dt} \\ & = \frac{\mathrm{d}v }{\mathrm{d}t} \mathbf{u}_\mathrm{t} +v(t)\frac{d \mathbf{u}_\mathrm{t}}{dt} \\ & = \frac{\mathrm{d}v }{\mathrm{d}t} \mathbf{u}_\mathrm{t}+ \frac{v^2}{R}\mathbf{u}_\mathrm{n}\ , \\ \end{alignat}

    where un is the unit (inward) normal vector to the particle's trajectory, and R is its instantaneous radius of curvature based upon the osculating circle at time t. These components are called the tangential acceleration and the radial acceleration or centripetal acceleration (see also circular motion and centripetal force).

    Extension of this approach to three-dimensional space curves that cannot be contained on a planar surface leads to the Frenet–Serret formulas.[5][6]

    Special cases

    Uniform acceleration

    Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an equal amount in every equal time period.

    A frequently cited example of uniform acceleration is that of an object in free fall in a uniform gravitational field. The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g (also called acceleration due to gravity). By Newton's Second Law the force, F, acting on a body is given by:

    \mathbf {F} = m \mathbf {g}

    Due to the simple algebraic properties of constant acceleration in the one-dimensional case (that is, the case of acceleration aligned with the initial velocity), there are simple formulas that relate the following quantities: displacement, initial velocity, final velocity, acceleration, and time:[7]

    \mathbf {v}= \mathbf {u} + \mathbf {a} t
    \mathbf {s}= \mathbf {u} t+ {{1} \over {2}} \mathbf {a}t^2 = {{(\mathbf{u}+\mathbf{v})t} \over {2}}
    |\mathbf {v}|^2= |\mathbf {u}|^2 + 2 \, \mathbf {a} \cdot \mathbf {s}

    where

    \mathbf{s} = displacement
    \mathbf{u} = initial velocity
    \mathbf{v} = final velocity
    \mathbf{a} = uniform acceleration
    t = time.

    In the case of uniform acceleration of an object that is initially moving in a direction not aligned with the acceleration, the motion can be resolved into two orthogonal parts, one of constant velocity and the other according to the above equations. As Galileo showed, the net result is parabolic motion, as in the trajectory of a cannonball, neglecting air resistance.[8]

    Circular motion

    Uniform circular motion is an example of a body experiencing acceleration resulting in velocity of a constant magnitude but change of direction. In this case, because the direction of the object's motion is constantly changing, being tangential to the circle, the object's velocity also changes, but its speed does not. This acceleration is directed toward the centre of the circle and takes the value:

    a = {{v^2} \over {r}}

    where v is the object's speed. Equivalently, the radial acceleration may be calculated from the object's angular velocity \omega, whence:

    \mathbf {a}= {-\omega^2} \mathbf {r}.

    The acceleration, hence also the force acting on a body in uniform circular motion, is directed toward the center of the circle; that is, it is centripetal – the so called 'centrifugal force' appearing to act outward on a body is really a pseudo force experienced in the frame of reference of the body in circular motion, due to the body's linear momentum at a tangent to the circle.

    Relation to relativity

    "The force one feels from gravity and the force one feels from acceleration are the same. They are equivalent. Einstein called this the principle of equivalence. Since gravity and acceleration are equivalent, if you feel gravity's influence, you must be accelerating. Einstein argued that only those observers who feel no force at all - including the force of gravity - are justified in declaring that they are not accelerating."[9]

    See also

    References

    1. ^ Crew, Henry (2008). The Principles of Mechanics. BiblioBazaar, LLC. pp. 43. ISBN 0-559-36871-2. 
    2. ^ Bondi, Hermann (1980). Relativity and Common Sense. Courier Dover Publications. pp. 3. ISBN 0-486-24021-5. 
    3. ^ Lehrman, Robert L. (1998). Physics the Easy Way. Barron's Educational Series. pp. 27. ISBN 0-7641-0236-2. 
    4. ^ http://mathworld.wolfram.com/ChainRule.html
    5. ^ Larry C. Andrews & Ronald L. Phillips (2003). Mathematical Techniques for Engineers and Scientists. SPIE Press. p. 164. ISBN 0-8194-4506-1. http://books.google.com/books?id=MwrDfvrQyWYC&pg=PA164&dq=particle+%22planar+motion%22#PPA164,M1. 
    6. ^ Ch V Ramana Murthy & NC Srinivas (2001). Applied Mathematics. New Delhi: S. Chand & Co.. p. 337. ISBN 81-219-2082-5. http://books.google.com/books?id=Q0Pvv4vWOlQC&pg=PA337&vq=frenet&dq=isbn=8121920825. 
    7. ^ Keith Johnson (2001). Physics for you: revised national curriculum edition for GCSE (4th ed.). Nelson Thornes. p. 135. ISBN 978-0-7487-6236-1. http://books.google.com/books?id=D4nrQDzq1jkC&pg=PA135&dq=suvat#v=onepage&q=suvat&f=false. 
    8. ^ David C. Cassidy, Gerald James Holton, and F. James Rutherford (2002). Understanding physics. Birkhäuser. p. 146. ISBN 978-0-387-98756-9. http://books.google.com/books?id=iPsKvL_ATygC&pg=PA146&dq=parabolic+arc+uniform-acceleration+galileo#v=onepage&q=parabolic%20arc%20uniform-acceleration%20galileo&f=false. 
    9. ^ Brian Greene, The Fabric of the Cosmos, page 67. Vintage ISBN 0-375-72720-5

    External links

    Wikimedia Commons has media related to: Acceleration

    ← Integrate … Differentiate →

    Displacement (Distance) | Velocity (Speed) | Acceleration | Jerk | Jounce

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    Translations:

    Acceleration

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    Dansk (Danish)
    n. - acceleration, hastighedsforøgelse

    Nederlands (Dutch)
    versnelling, bespoediging

    Français (French)
    n. - accélération, (Fin) (clause) d'accélération, (Fin) remboursement, par déchéance du terme

    Deutsch (German)
    n. - Beschleunigung, Vorverlegung, Akzeleration

    Ελληνική (Greek)
    n. - επιτάχυνση, επίσπευση

    Italiano (Italian)
    accelerazione

    Português (Portuguese)
    n. - aceleração (f)

    Русский (Russian)
    ускорение

    Español (Spanish)
    n. - aceleración

    Svenska (Swedish)
    n. - acceleration

    中文（简体）(Chinese (Simplified))
    加速, 加速度, 促进

    中文（繁體）(Chinese (Traditional))
    n. - 加速, 加速度, 促進

    한국어 (Korean)
    n. - 촉진, 가속도

    日本語 (Japanese)
    n. - 加速, 促進, 加速度

    العربيه (Arabic)
    ‏(الاسم) تسريع, تعجيل‏

    עברית (Hebrew)
    n. - ‮תאוצה, האצה‬

    If you are unable to view some languages clearly, click here.


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