Definition

• In the language running, acceleration is Synonyme with going more quickly. Generally, acceleration indicates the increase in the Speed of the evolution of an unspecified process. Example: acceleration of the cardiac rhythm, acceleration of the events of a topicality, etc

• In physics and more precisely in kinematics, acceleration is a vector quantity which indicates for a movement, if its speed is constant, increasing or decreasing.

If we take account of the definition of the Speed, it then becomes possible to affirm that acceleration is the report/ratio which measures the evolution speed at time. Simply known as, acceleration expresses the speed with which the speed of a mobile varies.

Applications

In the everyday life, one distinguishes three events which the physicist gathers under the only concept of acceleration :

• more quickly to go (to accelerate with the more restrictive common direction: acceleration is positive, i.e. the vector acceleration has a component in the direction speed),
• less quickly to go ( to slow down or to decelerate or slow down in the common language: acceleration is negative, or the vector acceleration has a component opposed within the meaning of speed)
• and to change direction (to turn or transfer in the common language: acceleration is perpendicular at the speed, if this one changes direction without changing standard)

Calculation of the distance covered

For example, you wish to calculate the distance covered by a solid moving accelerated, if acceleration $a$ is constant. In the formula below, $d\_0$ represents initial displacement, $v\_0$ initial speed, $\backslash \; Delta\; t$ the journey time and $a$ acceleration:

$d\; =\; d\_\; \{0\}\; +v\_\; \{0\}\; \{\backslash \; Delta\; T\}\; +\; has\; \backslash \; frac\; \{2\}$

Example

In order to determine the height of a bridge, one releases a stone since the top of the aforesaid bridge. This one spends 2,5 seconds to reach the ground. Which is the distance covered?

One must hold account that:

• initial speed is null;
• gravitational acceleration is of 9,81  m·S −2 ;
• one neglects the friction of the air which proportionally reduces acceleration at the instantaneous speed. ;

$d\; =\; 0\; \backslash \; times\; 2,5\; +\; \backslash \; frac\; \{9,81\; \backslash \; times\; 2.5^2\}\; \{2\}\; =\; 30,656\; \backslash \; \backslash \; mathrm\; \{m\}$

Acceleration in dynamic mechanics

In Dynamic, acceleration $\backslash \; overrightarrow\; \{has\}$ undergone by a body is related to the force $\backslash \; overrightarrow\; \{F\}$ total exerted on this one via the second law of Newton (or basic principle of dynamics ) according to which

$\backslash \; overrightarrow\; \{has\}\; =\; \backslash \; frac\; \{1\}\; \{m\}\; \backslash ,\; \backslash \; vec\; \{F\}$

where m is the mass of the corps.
This equation means that any force applied to an object produces an acceleration automatically, whatever the mass of this object.

Average acceleration

The average acceleration has on an time interval ΔT is in the following way defined:

$has\; =\; \backslash \; frac\; \{v\_2\; -\; v\_1\}\; \{t\_2\; -\; t\_1\}\; =\; \backslash \; frac\; \{\backslash \; Delta\; v\}\; \{\backslash \; Delta\; T\}$

v₁ is speed at the moment t₁ and v₂ is speed at the moment t₂ .

Acceleration and revolved

The Gravité causes the acceleration of a mass which is subjected only to this only force, at the time of the movement which by definition is called the Freefall. The intensity of the gravity undergone by a body is thus expressed in the form of an acceleration, noted $\backslash \; vec\; \{G\}$. In order to give a value “  parlante  ”, one often expresses an acceleration compared to the average acceleration of gravity on Earth, in G  :

$g\; =\; 9,80908285\; \backslash \; \backslash \; mathrm\; \{m\; \backslash ,\; s^\; \{-\; 2\}\}$

The General relativity establishes that the force of Gravité is not locally distinguished (i.e. if one considers only one point) from an acceleration, and that this is why Masse of Gravitation and masses Inertie cannot be distinguished functionally. It is important on the conceptual level to know this equivalence, much physicists using for this reason, in summary, the term acceleration indifferently to indicate a modification speed or the presence in a field of gravity, even in the apparent absence (in space 3D) of movement.

Variations of acceleration

Just like the vector acceleration is the derivative of the Flight Path Vector compared to time one can define the derivative of acceleration compared to time. It is about the vector Jerk which thus makes it possible to quantify the variations of acceleration and which is used in a certain number of fields.

Acceleration of convergence in Mathematics

The term is also used in Mathématiques, for example the acceleration of the convergence of a continuation (by processes as the Delta-2 of Aitken) means that the difference between the value of the elements of the continuation and its limit is smaller than for the initial continuation with a row N given.

See too

• Accélération of Siacci
• Instantaneous acceleration
• Accélération centrifuges
• Angular acceleration
• Accéléromètre

Simple: Acceleration Zh-min-nan: Ka-sok-tō͘

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