Define acceleration,average acceleration,and instantaneous acceleration.

(N/A) Acceleration is defined as the time rate of change of velocity.
Average acceleration is the change in velocity divided by the time interval during which the change occurs. If a particle has velocities $v_{1}$ and $v_{2}$ at times $t_{1}$ and $t_{2}$ respectively,the average acceleration $\langle a \rangle$ is given by:
$\langle a \rangle = \frac{v_{2} - v_{1}}{t_{2} - t_{1}} = \frac{\Delta v}{\Delta t}$
Average acceleration is a vector quantity,and its direction is the same as the direction of the change in velocity $\Delta v$.
Instantaneous acceleration $a$ is defined as the limit of the average acceleration as the time interval $\Delta t$ approaches zero:
$a = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t} = \frac{dv}{dt}$
It represents the acceleration of an object at a specific instant of time.