Well all we have to do is remind ourselves that the change in velocity the change in velocity which is the same thing as the final velocity minus the initial velocity so the final velocity, remember, we're just talking about half of the path of this ball so the time that get's released and it goes and its, and it's going as kind of it's maximum upward velocity it goes slower and slower and slower all the way until it's stationary for just a moment then starts going down again, remember the acceleration is costed downwards this entire time so what is the final velocity if we just consider half of this time well the time is zero so it's going to be zero minus our inicial velocity, minus our inicial velocity when it was taking off thats our change in velocity this is our change in velocity, this is our change in velocity is going to be equal to the acceleration of gravity the acceleration of gravity now negative nine point eight meters per second square or the acceleration due to gravity when an object is in freefall to be technicaly correct times, times, times the time we are going up so times delta T up witch is the same thing