# Acceleration

Acceleration:

When the velocity of a particle changes then it is said to undergo acceleration.

Acceleration is a vector quantity.

When velocity of the object increases then the acceleration is positive and when velocity decreases the acceleration is negative and is called deceleration.

Mathematically,

For an motion along an axis:

Average acceleration = $a_{avg} = \dfrac{v_2 - v_1}{t_2 - t_1}$

Where , “v2″ is the velocity at time “t2″ and “v1″ is the velocity at time “t1″.

And the limiting value of the average acceleration as $t_2 - t_1 = \Delta t$ tends towards zero , is called instantaneous acceleration or simply acceleration.

Mathematically,

Acceleration = $\displaystyle\lim_{\Delta t\to 0}\frac{\Delta v}{\Delta t}$

Or, Acceleration of a particle at a given constant is the rate of change of velocity at the instant. And acceleration is the derivative of  velocity of a particle and the second derivative of  it’s position( x ).

Mathematically:

Acceleration = $\frac{d}{dx} v = \frac{d^2}{dx^2} x$

unit: The unit of acceleration in which it’s mathematical value is expressed is “meters per second squared” $\frac{m}{s^2}$ or , length per time squared. $\frac{L}{T^2} = LT^{-2}$

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