Final answer:
The two relationships for the accelerations of two blocks in absolute dependent motion are a₁x = −a₂y and |a₁| = |a₂|, highlighting the equal magnitude of acceleration regardless of direction and the principle of the independence of motion.
Step-by-step explanation:
The two equally correct relationships between the acceleration components of two blocks in absolute dependent motion in the x-direction are as follows: First, when block 1 moves to the right, block 2 moves downward, which means a₁x = −a₂y. This highlights the equal magnitude but opposite directions of acceleration, assuming the string connecting them remains taut. Second, the magnitudes of acceleration are equal, |a₁| = |a₂|, indicating that although the blocks are moving in perpendicular directions, the acceleration of each block is the same when measured in absolute terms.
Independent motion in two dimensions suggests that motion in the horizontal direction doesn't affect motion in the vertical direction, and vice versa. Thus, any force causing acceleration in one block must equally affect the other, regardless of their individual motion paths. This concept is encapsulated in the independence of motion principle of two-dimensional motion.