Final answer:
The statement is false because in non-uniform circular motion, both centripetal acceleration and tangential acceleration are present, the latter due to a changing speed, resulting in a total acceleration that is not constant in magnitude or direction.
Step-by-step explanation:
The statement that in a non-uniform circular motion the centripetal acceleration is constant in magnitude and has a fixed direction is false. In non-uniform circular motion, there is also a tangential acceleration present due to the changing speed of the object, which alters the total acceleration of the object.
Centripetal acceleration, which points toward the center of rotation and is defined by the equation ac = v²/r, must always point radially inward regardless of whether the motion is uniform or non-uniform. However, in non-uniform circular motion, the magnitude of the centripetal acceleration can change if the speed of the object changes. The total acceleration is the vector sum of the tangential and centripetal accelerations.