Mathematically instantaneous velocity of an object is the limiting value of average velocity as tends towards 0.

Or:

Instantaneous velocity =

And instantaneous velocity is also the derivative of the “position of the object” ( “x” ) with respect to “time interval”( “t” )

or, Instantaneous velocity =

In a graph of motion of an object drawn “x” versus “t”; Instantaneous velocity of the object is the slope of tangent line drawn at the position representing that instant.

Instantaneous velocity is a vector quantity and thus have it’s direction ( positive or negative ) associated with it along with it’s magnitude.