* The Relationship: Final velocity (vf) is determined by initial velocity (vi), acceleration (a), and time (t) through the following equation:

vf = vi + at

* Scenario 1: Constant Acceleration: If an object is slowing down (decelerating), the acceleration will be in the opposite direction of the initial velocity. In this case, the final velocity can be zero even if the initial velocity was quite high. Think of a car coming to a stop.

* Scenario 2: Changing Acceleration: Even if the acceleration is not constant, you can still have a final velocity of zero. For example, imagine a ball thrown straight up in the air. The initial velocity is upward, but gravity acts as a downward acceleration. At the peak of its trajectory, the ball's velocity is momentarily zero before it starts falling back down.

Key Point: The only way the initial velocity *cannot* be different from zero if the final velocity is zero is if there's no acceleration at all. If an object is not accelerating, it maintains a constant velocity.