We present a thermal broadband noise from the difference between two Ornstein-Uhlenbeck noises, which can induce a ballistic diffusion, i.e., long-time mean square displacement of a free particle driven by this noise reads <x(2)(t)> proportional to t(2). We apply this noise to a flashing ratchet and the mean velocity of the particle is calculated via Langevin simulation. The results show that a double peak of the mean velocity and flux reversal appears for the ratchet with large and small asymmetries, respectively; the inertia effect induces a large mean velocity and multireversal of flux. These rich and interesting phenomena are explained.