1) The document presents the solution to determining the horizontal acceleration (ẍ) of a bead moving along a curved wire with potential energy V(x). 2) It derives an expression for ẍ as ẍ = −(g + ÿ)V, where ÿ is the vertical acceleration of the bead. 3) For a stationary wire, ÿ reduces to V̈, the second derivative of the potential energy. But for a vertically moving wire, ÿ simply represents the vertical acceleration of the bead relative to the ground.