The velocity of a comet increases as it approaches planets due to gravitational acceleration from the sun and the planets themselves. As the comet gets closer, the gravitational interaction intensifies, leading to increased acceleration and velocity. This phenomenon is explained by the conservation of energy, where the comet gains speed as it moves deeper into the gravitational field, akin to an object falling down a gravity well. Additionally, Kepler's laws indicate that the area swept by celestial bodies remains constant, necessitating an increase in speed as the comet's distance to the sun decreases. Overall, the comet's acceleration and velocity are influenced by the gravitational forces at play.