An object with an initial velocity of zero and non-zero acceleration will begin to move from rest and continue to accelerate according to Newton's laws. The discussion highlights that the specific nature of the acceleration, such as whether it is due to gravity or another force, is not specified but is crucial for understanding the motion. Participants agree that the object's velocity will change as it accelerates. The analogy of a car starting from rest and increasing speed is used to illustrate this concept. Overall, the motion of the object is characterized by a continuous increase in velocity.