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Time rate of change of velocity = acceleration

If acceleration is constant in magnitude and direction, that means the force acting on a body is constant.  Some thing like electromagnetic force in a uniform electromagnetic field.  It is possible when one (net) force is acting on an object.

Gravitational force on a particle when no other acts - it is the case of a projectile motion in two dimensions.  The projectile changes velocity in vertical direction and has a constant horizontal velocity. So its total velocity changes in magnitude and direction all the time.  acceleration is always vertically downwards and constant at g.

In a motion along a straight line acceleration can be constant , but velocity does not change in direction at each instant.  In a circular motion, acceleration or change of velocity - is not constant. it changes direction towards the radius always.
It is constant only in magnitude.