Achild throws a ball up in the air to a height of 3.5 m and catches it at the same point from which he threw it. the ball is in the air for a total of 1.7 s. what is the average velocity of the ball?

You're not going to like this answer, and you'll think it's wrong.  But it isn't.

"Velocity" is not "Speed".  "Velocity" has a very precise definition, which
can be stated like this:

Velocity =
(straight distance between the start point and end point)
      divided by
(the length of time it took to get there).
     and
(the direction from the start point to the end point).

Notice that it doesn't say anything about the route traveled between the
start point and the end point, only the straight distance between them.

Now . . . The boy tossed the ball straight up, it went up for a while, then
it fell back down, and he caught it in the same hand he threw it with.

The ball traveled for 1.7 seconds.  It went 3.5 meters up, and 3.5 meters
down.  BUT the start and end points were both the same place ... his hand.
The distance between the start and end points is . . . zero.

So the average velocity of the ball during that time is . . . zero .