If the velocity of a particle remains constant as time passes, we say that it is moving with uniform velocity. If the velocity changes with time, it is said to be accelerated.**The acceleration is the rate of change of velocity**.

Velocity is a vector quantity hence a change in its magnitude or direction or both will change the velocity, which means if even direction of velocity of an object is changing then its accelerating.

Suppose that velocity of a particle at time t_{1} is v_{1} vector and at time t_{2} is v_{2} vector. The change produced in time interval t_{1} to t_{2} is v_{2} vector – v_{1} vector.

We define the Average Acceleration a_{av} vector as change in velocity divided by time interval.

The average acceleration depends only on the velocities at time t_{1} and t_{2}. How the velocity changed in between t_{1} and t_{2} is not important in defining the average acceleration.

On the other hand, Instantaneous Acceleration of a particle at time t is defined as

Where Δv vector is change in velocity between time t and t + Δt.