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? explain your answer.

This question is either poorly written or else it's very sneaky.

First, let's talk about the average speed of the ball.
Speed is  (distance traveled) / (time to travel the distance).
For this ball, the distance traveled is 3.5m up and 3.5 m down = 7 m.
Average speed = (distance) / (time) = 7 / 1.7 = 4.12 m/s .

Now, let's talk about velocity.  It's not the same thing as speed.
Velocity is 
          (distance between the start and end points) / (travel time)
and it also includes the direction from the start point to the end point.
The child caught the ball at the same place from which he threw it, so
the distance between the start and end points is zero, and the average
velocity is zero.

The only thing left to do is decide whether the question is sneaky or
poorly written.  Using a little bit of Physics, we know that on Earth,
a ball tossed to a maximum height of 3.5 m and then caught on the
way down actually does spend almost exactly 1.7 s in the air.  Since
the question is accurate in that regard, I'm going to guess that it's
sneaky ...  It knows very well the difference between speed and velocity,
and it's testing to find out whether you know the difference too.

The correct answer would be b