acceleration

1. 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.

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.
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.
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.

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.

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

For more information on acceleration, visit Britannica.com.

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.

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.

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.

A change in the velocity of an object.

"Accelerate" redirects here. For other uses, see Accelerate (disambiguation).

For the waltz composed by Johann Strauss, see Accelerationen.

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 a_t is due to the change in speed of traversal, and points along the curve in the direction of the velocity vector. The centripetal component a_c 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.

In physics, and more specifically kinematics, acceleration is the change in velocity over time.^[1] Because velocity is a vector, it can change in two ways: a change in magnitude and/or a change in direction. In one dimension, i.e. a line, acceleration is the rate at which something speeds up or slows down. However, as a vector quantity, acceleration is also the rate at which direction changes.^[2][3] Acceleration has the dimensions L T⁻². In SI units, acceleration is measured in metres per second squared (m/s²).

In common speech, the term acceleration commonly is used for an increase in speed (the magnitude of velocity); a decrease in speed is called deceleration. In physics, a change in the direction of velocity also is an acceleration: for rotary motion, the change in direction of velocity results in centripetal (toward the center) acceleration; where as the rate of change of speed is a tangential acceleration.

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

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

Contents 1 Average and instantaneous acceleration 2 Tangential and centripetal acceleration 3 Relation to relativity 4 Notes 5 See also 6 External links

Average and instantaneous acceleration

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.

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:

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

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 u_t, the acceleration of a particle moving on a curved path on a planar surface can be written using the chain rule of differentiation as:

where u_n is the unit (outward) 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, respectively. The negative of the radial acceleration is the centripetal acceleration, which points inward, toward the center of curvature.

Extension of this approach to three-dimensional space curves that cannot be contained on a planar surface leads to the Frenet-Serret formulas.^[4][5]

Relation to relativity

After completing his theory of special relativity, Albert Einstein realized that forces felt by objects undergoing constant proper acceleration are actually feeling themselves being accelerated, so that, for example, a car's acceleration forwards would result in the driver feeling a slight push backwards. In the case of gravity, which Einstein concluded is not actually a force, this is not the case; acceleration due to gravity is not felt by an object in free-fall. This was the basis for his development of general relativity, a relativistic theory of gravity.

Notes

1. ^ Crew, Henry (2008). The Principles of Mechanics. BiblioBazaar, LLC. pp. 43. ISBN 0559368712. 
2. ^ Bondi, Hermann (1980). Relativity and Common Sense. Courier Dover Publications. pp. 3. ISBN 0486240215. 
3. ^ Lehrman, Robert L. (1998). Physics the Easy Way. Barron's Educational Series. pp. 27. ISBN 0764102362. 
4. ^ Larry C. Andrews & Ronald L. Phillips (2003). Mathematical Techniques for Engineers and Scientists. SPIE Press. p. 164. ISBN 0819445061. http://books.google.com/books?id=MwrDfvrQyWYC&pg=PA164&dq=particle+%22planar+motion%22&lr=&as_brr=0&sig=ACfU3U2LpH6ofhuuC2UiED0pf38wbspY8A#PPA164,M1. 
5. ^ 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&source=gbs_search_s&sig=ACfU3U3S5vGMS-NnraAEmpBf6B9bB2wK6A. 

See also

• Uniform acceleration
• Angular acceleration
• Gravitational acceleration
• Coordinate vs. physical acceleration
• Derivatives of position
• Equations of Motion
• Proper Acceleration
• 0 to 60 mph
• Shock (mechanics)
• Specific force

External links

Wikimedia Commons has media related to: Acceleration

• 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
• Acceleration Converter Converts common acceleration units.

v • d • e Kinematics ← Integrate … Differentiate → Displacement (Distance) | Velocity (Speed) | Acceleration | Jerk | Snap | Crackle and pop

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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

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