Final answer:
The relationship between the accelerations of blocks A and B, when attached by a taut, ideal string, is that both blocks have the same acceleration. This is because a change in acceleration for one block would break the tautness of the string or lose contact, hence maintaining equal acceleration for both.
Step-by-step explanation:
The relationship between the accelerations of blocks A and B can be understood by considering that when blocks are connected by a string, pulley, or through some form of contact mechanism allowing them to move together, they must accelerate at the same rate. That is, assuming the string remains taut and the system is only under the influence of the forces mentioned, both blocks have the same acceleration (c). For instance, suppose two blocks are connected by a string over a pulley, and each block is subjected to different forces. If the magnitudes of forces A and B are such that the system moves with a constant acceleration, the blocks will share this same acceleration since a change in acceleration for one would break the tautness of the string or lose contact. This is further reinforced if the string and pulley are considered ideal, meaning they have no mass and do not stretch, which is often an assumption in physics problems. Additionally, free-body diagrams provide a visual representation of the forces acting upon each block. Through these diagrams, one can analyze the forces and if they balance out, the blocks would move with the same acceleration. The tension in the string, which often requires solving a system of equations, would also be the same for both blocks due to the nature of tensions in an ideal string. However, if the conditions of the string or the surface are not ideal, more information might be needed to determine the exact relationship of their accelerations. Yet for most introductory physics problems, we typically assume the string and pulley are ideal.