If someone were to throw an object vertically, and catch it as it returned back down, describe how the velocity vector of this object changes over this period.

On the way up:

The velocity vector starts out with some magnitude when it leaves my hand. It shrinks and shrinks and shrinks as the object rises, losing 9.8 m/s of speed every second, and becoming zero at the top of the arc. The vector points straight up all the way.

At the top:

The vector instantly snaps around, stops pointing up, and starts pointing down.

On the way down:

The vector grows and grows and grows as the object falls, gaining 9.8 m/s of speed every second. Just as it reaches the speed with which it left the hand, it plops back into the hand. The vector points straight down all the way.