See the coast clear'd, and then we will depart.
Good God, these nobles should such stomachs bear!
I myself fight not once in forty year.
I was driving down the coast, and I started thinking about the forms of that word: the coast of the ocean, coaster brakes on a bike, coasting down a hill, a coaster for your drink, coasting in your life (cough), and such like.
My pile of etymological books says that the word comes from the Latin costa, rib, and thus side or flank. This survives in anatomical terms, as in intercostal, between the ribs. Thus, the side of the land is the coast, and was once applied to rivers as well as larger bodies of water, especially the lower Mississippi.
The French also used it to describe the side of a hill, and in North America this described a slope down which one rode a sledge (later, sled) in the snow. In time, one coasted down the snow-covered hill, and that usage led to the sense of riding without power in wheeled vehicles like bicycles or automobiles.
By extension, anything we do without effort is coasting, as in "she coasted by on her good looks." Nelson Algren, in The Man with the Golden Arm, used coasting to refer to intoxication, whether by drugs or music. Here, Frankie Machine visits his dealer to ease his withdrawal pain:
In the early 20th century, coaster was a generic and branded term for toy wagons, which were put to use when the snow had melted (not unlike the development of skateboards as street versions of surfboards).
In some places, snow sleds were also branded as coasters, especially those I think of as saucers.
Rollercoasters are another branch of the tree. The idea of coasting railcars down inclined railways predates the term rollercoaster, but which came first, sleds or rails?
A couple guesses on origins I can't find evidence for: a coaster brake on a bicycle, maybe because the braking action was applied to the freewheel rather than the tire or rim; and coaster for a drink, probably similar coasters for furniture, which go under the legs to help avoid scratching the floors.
Other word relatives: accost, come up to the side of; cutlet, a small rib, derived from French cotelette; and costermonger, an apple-seller, from an apple with prominent ribs called a Costard.
Finally, "the coast is clear" gets used by Shakespeare (as "the coast clear'd" in the excerpt from Henry VI above, and later in Twelfth Night). The phrase predates him, first referring to a ship having safely sailed away from the coast, but Shakespeare's use is more in line with the modern sense of "there's no one watching us," which seems to have taken on the connotation of smugglers unloading a ship of contraband.
There, having cleared coast from my brain, I'll get back to work.