A constant power machine pulls a block on a smooth horizontal surface. Which one of the following correctly describes the relation between speed of the block (v) and time (t)?

Constant power means P = Fv = (m dv/dt)v = constant. Hence m v dv = P dt. Integrating from 0 to v on the left and 0 to t on the right gives (1/2)m v² = P t, so v² ∝ t and v ∝ √t. This is the standard result for motion under constant power from rest on a frictionless surface.