While the ball falls, gravity speeds it up at a constant rate. When acceleration is constant, position changes with time according to this equation:
y = y₀ + v₀t + ½at²
The app finds the curve y = At² + Bt + C that comes closest to all of your points. That's the line drawn on the graph. It picks A, B, and C so that the vertical gaps between the curve and your points, squared and added up, are as small as possible.
Matching the two equations term by term:
- C matches y₀, the starting position. It comes out near 0 because your first mark is the origin.
- B matches v₀, the ball's velocity at your first mark. It isn't 0 because you started marking after the ball was already falling.
- A matches ½a. So the acceleration is a = 2A.