Question

What’s is a object that moves through the air space acted on only by gravity

Answer 1

This describes projectile motion while neglecting any outside forces other than gravity

Answer 2

I believe the answer is projectile
As the object reach its maximum height after it thrown, its speed will falls into 0. But due to the gravity force, the speed of the object will start to accelerate again after it came down until it hit another medium.
Example of projectiles: a thrown baseball, a catapult shot.