The dipole polarizabilities of the potassium atom in its ground (4 S-2) and low-lying excited (4 P-2, 5 S-2) states have been calculated using the time-dependent gauge-invariant variational method [Merawa, Rerat, and Pouchan, J. Chim. Phys. 91, 1387 (1994)]. The variation of these polarizabilities versus imaginary frequencies [Casimir and Polder, Phys. Rev. 73, 360 (1948)] have been computed, and the long-range dispersion coefficients for the molecular states of K-2 dissociating to K(4S)+K(4S), K(4S)+K(4P), K(4P)+K(4P), K(4S)+K(5S), K(5S)+K(4P) and K(5S)+K(5S) have been evaluated. The results obtained for K(4S)+K(4P) interactions are in very good agreement with the recent experimental high-resolution photoassociative data of Wang et al. [J. Chem. Phys. 106, 7899 (1997)]. The long-range dispersion coefficients for the K(4P)+K(4P), K(4P)+K(5S) and K(SS)+K(SS) interactions are new.