Here's why:

* Acceleration is the rate of change of velocity.

* Maximum velocity implies the object is no longer speeding up.

* If the velocity is not changing, then the rate of change of velocity (acceleration) is zero.

Think of it this way:

Imagine a car speeding up. It has positive acceleration. When it reaches its maximum speed, it stops accelerating. At that moment, its velocity is not changing, so its acceleration is zero.

Important Note: This only applies to *instantaneous* maximum velocity. If the object is moving at its maximum speed for a sustained period, it may still be accelerating in a different direction (e.g., turning a corner).