Acceleration is defined as the rate of change of velocity over time. In classical physics, acceleration refers to a continuous change in velocity. According to the laws of physics, velocity cannot change instantaneously or suddenly without an external force or an impulse acting on an object.
However, in certain situations, it may appear as if velocity or acceleration changes suddenly due to practical limitations in measurements or the presence of very short-duration events. For example, when observing the motion of an object with limited precision or using discrete measurements, the velocity or acceleration values may appear to change abruptly. But in reality, there would still be an underlying continuous process of change.
It's important to note that abrupt changes in velocity or acceleration often indicate the presence of external forces or events such as collisions, explosions, or instantaneous impulses. In such cases, the change in velocity or acceleration occurs rapidly but not instantaneously.