Acceleration

The acceleration of a particle is defined, conceptually, as the rate at which the velocity of the object is changing. Mathematically, if we are given the position function (on a number line, for example) of an object with respect to time, $x(t)$, the acceleration of the object is given by $$a(t) = \frac {\mathrm{d}^2x}{\mathrm{d}t^2} = x''(t).$$(Also the derivative of the velocity function.)

Like velocity, acceleration is a vector.

There a few different types of acceleration one can use to describe an object. The first is instantaneous acceleration. Instantaneous acceleration as the limit of average acceleration for short time intervals. In other words, it is the derivative of the velocity function at that particular instant.

Average velocity is defined as the change in velocity of an object over a certain elapsed time period divided by the elapsed time.

Rate of change of velocity is called acceleration.

$$a=\frac{{d}v}{ {d}t}$$

Acceleration is a vector quantity.

Acceleration is positive if it is in the direction of velocity, and it is negative if it is in opposite direction to velocity (motion).

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Acceleration is the second derivative of position, or the change in velocity. Acceleration is a vector, generally expressed in meters per second^2. Understand that meters per second squared is just a simplification of (meters per second)per second. An acceleration of 5 m/s^2 means that every second, the object' velocity increases by 5 m/s.