Particle Acceleration

To accelerate an object (air particle) is to change its velocity over a period of time. Acceleration is defined technically as "the rate of change of velocity of an object with respect to time" and is given by the equation
:

\mathbf{a} = {d\mathbf{v}\over dt}

where

''a'' is the acceleration vector

''v'' is the velocity vector expressed in m/s

''t'' is time expressed in seconds.

This equation gives ''a'' the units of m/(s·s), or m/s² (read as "metres per second per second", or "metres per second squared").

An alternative equation is:
:

\mathbf{\bar{a}} = {\mathbf{v} - \mathbf{u} \over t}

where

\mathbf{\bar{a}}

is the average acceleration (m/s²)

\mathbf{u}

is the initial velocity (m/s)

\mathbf{v}

is the final velocity (m/s)

\mathbf{t}

is the time interval (s)

Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get a Circular Motion . For this Centripetal Acceleration we have

:

\mathbf{a} = - rac{v^2}{r} rac{\mathbf{r}}{r} = - \omega^2 \mathbf{r}

One common unit of acceleration is '' G '', one ''g'' being the acceleration caused by the Gravity of Earth at Sea level at 45° latitude (Paris), or about 9.81 m/s².

In Classical Mechanics , acceleration

a \

is related to Force

F \

and Mass

m \

(assumed to be constant) by way of Newton's Second Law :
:

F = m \cdot a

Equations in terms of other measurements

The Particle acceleration of the air particles ''a'' in m/s² of a plain sound wave is:
:

a = \xi \cdot \omega^2 = v \cdot \omega = rac{p \cdot \omega}{Z} = \omega \sqrt rac{J}{Z} = \omega \sqrt rac{E}{
ho} = \omega \sqrt rac{P_{ak}}{Z \cdot A}

Information About

Particle Acceleration