Hello physics forum! As a youngster, it is a great honor to be surrounded by innocent minds. For this, thank you. Now, my question: I understand that the equation for vertical displacement caused by gravity is "y=0.5gt^2" or "y=-4.9t^2" in meters or"y=-16t^2" in feet. I have yet to understand why where is a 0.5 in the equation. It is to my understanding that if an object moves at for simplicity, 10 m/s, its displacement will increase by 10 m per second in the same direction. For example, an object in space throw initially at 5 m/s will travel 5 m in the first second, then 10 m away from the initial point in 2 seconds, and so forth. Gravity is a constant acceleration, by -9.8 m/s^2 or -32 ft/s^2. The velocity changes by these rates, depending on which unit. An object dropped will travel, in one second, -9.8 m/s downward, then -19.6 m/s, then -29.4 m/s. But when dealing with displacement, 0.5 is introduced...why?