Kinematics time question

For any physics free fall problem, a student is taught that the velocities on a graph have the same magnitude as those that are horizontally equivalent. For example, if you have two points that are both at the same height during free fall, one will be positive and the other will be negative--but they will be of the SAME magnitude.


Let's say we have a problem where an object was launched with a positive initial velocity in the upward direction. All we would have to do is change that upward initial velocity to downward (making it negative). Everything else stays the same, such as gravity.


Now here is the part where I get a bit confused. Why can we simply just use the inverse of the initial velocity without taking into account the time that has passed? Doesn't time start once the object leaves the starting point? If this is true, why can we use the same time for the kinematic equations?