An accelerometer measures proper acceleration, which is the acceleration experienced by an object due to forces acting on it, excluding gravity. During a ball's flight, the accelerometer reads zero because the ball is in free fall, experiencing no additional forces. When thrown upwards, the accelerometer detects increased acceleration as the ball is propelled, followed by a decrease to zero at the peak height, then a negative acceleration as it descends. The confusion arises from mixing up acceleration with velocity, as the expected trace should show distinct phases of acceleration during the throw and catch. For a pendulum, the accelerometer would show oscillations around the acceleration due to gravity, reflecting the forces of tension and gravity acting on it.