Yes, it is possible for both the initial velocity (u) and the final velocity (v) to be zero in certain situations. One such example is when an object is thrown straight up into the air and reaches its highest point, momentarily coming to a stop before falling back down. At the highest point of its trajectory, the object has a final velocity of zero, and when it is initially thrown, its initial velocity is also zero (assuming it was thrown from rest).
In this scenario, the object's velocity changes from an initial value of zero to a final value of zero, passing through zero in the process. However, it's important to note that the object's acceleration is not zero throughout its entire motion. Gravity acts on the object, causing it to slow down as it moves upward, reach a momentary stop, and then accelerate downward due to gravity.