Speed, accelerate, quicken, hasten, hurry, precipitate can mean to go or make go fast or faster.
Speed emphasizes rapidity of motion or progress; as a transitive verb it suggests an increase in tempo; as an intransitive verb, a high degree of swiftness.
Accelerate stresses increase in rate of motion or progress; it does not necessarily imply speed.
Quicken stresses shortening of the time consumed, often with a suggestion of animation or stimulation.
Hasten implies urgent quickness or a quick or premature outcome.
Hurry implies haste that causes confusion or prevents concentrated attention.
Precipitate implies impetuousness, suddenness, or abruptness.