An engine of a train, moving with uniform acceleration, passes the signal – post with velocity u and the last compartment with velocity $\upsilon .$  The velocity with which middle point of the train passes the signal post is:

Sign conventions are important because all kinematic variables can be positive or negative. You must first choose your coordinate system and positive direction, then consistently apply signs. For example, if you are choosing upward as positive in free-fall problems, gravity becomes negative (a = -g)

It's not always true. Direction of velocity is the most important consideration here that will tell us whether acceleration increases or decreases speed. You can consider two scenarios. If you're falling, that's negative velocity. That implies negative gravitational acceleration. Here, your speed in

Zero velocity doesn't mean zero acceleration. When you throw a ball-like object upward, at its peak the velocity is zero. But acceleration remains constant due to gravity. The velocity is still changing from positive to negative at that instant. That means acceleration continues.