Explain how race-based slavery developed during the seventeenth century. How did this impact the social and economic development of colonial America?

Over the course of the 17th century, slavery in American colonies gradually became more racial. In the first half of the 17th century, black slaves in Virginia could sometimes save enough tobacco to buy their freedom, purchase land and slaves, intermarry with whites, participate in law suits, and enlist in colonial militia.
A number of factors contributed to the emergence of racial slavery. During the second half of the 17th century, the Royal African Company and other slave merchants greatly increased the supply of African slaves to the Caribbean islands, where there was a sugar boom. In the 17th century, most black slaves came to the North American colonies from the Caribbean islands. Many small-scale white farmers left the Caribbean islands as large, slave-based plantations took over the sugar industry and local politics. The massive influx of African slaves to the Caribbean sugar islands, such as Barbados, prompted the English Parliament to introduce new legislation to provide legal cover for the ruthless suppression of black resistance. In 1667, the English Parliament adopted an Act to regulate the Negroes on the Plantations, demanding severe punishments for plantation slave workers. British courts during this time started to treat black people primarily as merchandise. These developments had an impact on the North American colonies as well.
In 1670, there were only about 2,000 black slaves in Virginia. By the end of the 17th century, Virginian planters had bought 4,000 more (see Blackburn 1997, 251). Nathaniel Bacon’s rebellion (1676) made the planters in Virginia recognize that black slaves could make common cause with poor white farmers; this prospect terrified them, and accordingly, they introduced racial legislation to sow a division between whites and blacks. In 1680, the Virginian House of Burgesses stipulated that if “any negro or other slave shall presume to lift up his hand in opposition to any christian” (as quoted in Blackburn 1997, 251), he would be punished by thirty lashes.
Virginia’s Act for Suppressing of Outlying Slaves (1691) authorized the killing of black and mixed race runway slaves, presumed that the great majority of the black and mixed race population was enslaved, and prohibited intermarriage between blacks, Native Americans, mixed race people; for whites, it was explicitly on racial grounds:

for the prevention of that abominable mixture and spurious issue which hereafter may increase in this dominion, as well as negroes, mulattoes and Indians intermarrying with English, or other white women . . . be it enacted . . . that for the time to come whatsoever English or other white man or woman being free shall intermarry intermarry with a negro, mulatto, or Indian man or woman, bond or free, shall within three months of such marriage be banished and removed from this dominion forever. (as quoted in Blackburn 1997, 264-265)

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Race-based slavery did not begin to develop as an official system until the 1690s. For a more thorough explanation of this development, I would recommend reading American Colonies by Alan Taylor. His chapter on Virginia is especially helpful in illustrating how and why the system developed.
Virginia is a helpful case study. It had the distinction of being the most prosperous colony, due to its successful tobacco trade. When tobacco became a less lucrative cash crop, the state successfully segued into cultivating cotton and became the young nation's wealthiest state, producing several US presidents, including plantation owner Thomas Jefferson.
Before the tobacco boom, Virginia's slaves enjoyed relative "freedom." They were allowed their own livestock and a small plot of land on which they cultivated their own small crops. The ability to maintain these bits of property tells us that the slaves enjoyed some leisure time and were granted a level of autonomy. Free blacks enjoyed a level of freedom that seemed to put them on par with whites. Not only could they own land, they could also testify in court and settle legal quarrels there; and they were permitted to marry whomever they chose. 
After the boom in the tobacco market, the lives of slaves and free blacks became more restricted to ensure the supply of free labor and to make black people the distinct source of that labor. To be white now meant to be a member of a privileged class. Poor whites benefited from this to some degree, as well. Taylor writes of instances in which poor white Virginians would steal livestock from blacks and go unpunished, due to the revocation of legal recourse for black people. 
Race-based slavery ensured the wealth of the white planter class, while the status of poorer whites did not change. Race-based slavery officially eliminated the necessity of white indentured servants. Earlier in the century, poor, but hopeful, British immigrants exchanged their labor for a parcel of land. This system created the unwelcome burden of market competition. Slave-based labor allowed planters to monopolize on lucrative agricultural markets. It also allowed for sharper divisions determined by class and race, creating the strict, "classical" hierarchy that characterized social and economic life in the South.