# Average Acceleration and Instantaneous Acceleration

**Average Acceleration **

For any change in velocity either in its magnitude or direction or both, acceleration must be present. Without acceleration neither magnitude nor direction of velocity can be changed.

When a particles velocity changes, the particle is said to undergo acceleration.

**Instantaneous Acceleration **

The Instantaneous Acceleration is derivative of the velocity with respect to time.

In words, acceleration of a particle at any instant is the rate at which its velocity is changing at that instant.

In words, the acceleration of a particle at any instant is second derivative of its position vector with respect to time.

Acceleration has both magnitude and direction. For motion on a straight line its algebraic sign represents its direction on an axis just as for displacement and velocity; that is, acceleration with a positive value is in the positive direction of an axis, and acceleration with a negative value is in the negative direction.