Give a step-by-step description of how a barrier island could form

The answer to your question is; Coastal sand is organized into barrier islands when three conditions are met:

Understanding the role of these conditions requires a little knowledge of coastal geology and oceanography. Coastal geology focuses on the rocks, sediments, and processes that form and shape the coastal zone. The processes involved range from the fracturing of the earth’s crust to form oceans to the seaward movement of sediment eroded from continents. Both ends of that range are important to us because the opening of the Atlantic Ocean created our coast and seaward movement of rock particles supplied the sand from which our coastal barrier islands were formed. Details of this process are described elsewhere (including the book mentioned on page 1), but for our purposes, suffice it to say that these processes endowed us with enough sand to form islands.

It is somewhat less obvious that barrier islands form only when sea level is rising, but if you look at coastlines that are rising faster than these, as in Newfoundland, you will not find barrier islands even though there is plenty of sediment to form them. Sea level is clearly rising along the Carolina coast and evidence of that fact is described in another field trip in this series (Evidence of Sea Level Rise: Coastal Erosion and Plant Community Changes).

The final condition for barrier island formation, winds and waves with sufficient energy to move sand, is met all along our coast and along most other coastlines around the world. Anyone who has visited a beach has seen waves washing sand grains up and down them, and most visitors have also seen wind-blown sand moving from the beach into the dunes. These phenomena are common because waves and wind almost always have enough energy to move sand grains. Waves derive this energy from wind blowing across the ocean surface. This energy is transported efficiently to the coastline where it dissipates into turbulence as the waves break. In this situation, the sea surface acts as an ocean-wide collector of wind energy, and surface waves deliver it to the beach where it can move sand around.

In addition, ocean winds first meet resistance above sea level at the shore, so fresh sea breezes can move fine-grained sand without any assistance by breakers. Together, these processes bring enough energy to move sand to the world’s coastlines. In some cases, the amounts of sand moved by wind and wave are both startling and destructive, as will be illustrated by photographs in this field trip and in the next one about high sand volume islands. 

I'm hoping this answers your question.

the right answer is 0.3 meters per second