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

Constant power P means P = Fv = (ma)v = m(dv/dt)v = constant. This gives m·v·dv = P·dt. Integrating: mv²/2 = Pt + constant. Assuming the block starts from rest at t=0, the constant is zero, so v² = 2Pt/m, which gives v ∝ √t. Therefore, option (b) is correct.