What are the definitions for average acceleration and instants acceleration?

Question

Not instants acceleration, instantanious acceleration. Sorry!

Answer 1

Of course, acceleration is the change in velocity over the change in time.

Average acceleration is the difference between velocities (∆v) at two discreet points, usually after (final) minus before (initial) as measured over some interval of time (∆t). Generally this is only meaningful when acceleration is constant. (You could also take the mathematical mean of the accelerations at different points, however this method is not very meaningful and is almost never used in physics.)

Average a = ∆v/∆t

Instantaneous acceleration is the difference between the final and initial velocities (dv) over an interval of time that is infinitesimally small (dt). (The limit as the interval approaches zero.) This becomes a derivative, the basis for differential calculus. Thus, the instantaneous acceleration is what the acceleration is at any point in time, usually expressed as a function (usually of time, but sometimes of position, velocity, etc.)

Instantaneous a = dv/dt

Answer 2

Acceleration is the change in velocity divided by the chang of time.

Average is a change in time of a measurable amount.
With the instant, the change in time is infinitely small.