Okay, you know how the acceleration of gravity changes by a factor of r^2 when you are falling downward from the sky to the ground. Say I drop a ball from b = 50 meters to a = 0 meters(surface of the earth). The change in acceleration over time is called a "jerk" and its the second derivative of velocity. So how could we calculate the actual final speed of the ball when it hits the surface of the earth including instantaneous acceleration? I know that it is negligible, but I want to see if its possible to really calculate excluding air resistance. I have an idea on how to start how to work this out, but I got a little confused because I am a little new to calculus and am not completely sure my work was correct. Using my intuition that a model of this would already exist if it was possible to make by other physicists.