Elongation of the polypeptide chain involves addition of amino acids to the carboxyl end of the growing chain. The growing protein exits the ribosome through the polypeptide exit tunnel in the large subunit.
Elongation starts when the fMet-tRNA enters the P site, causing a conformational change which opens the A site for the new aminoacyl-tRNA to bind. This binding is facilitated by elongation factor-Tu (EF-Tu), a small GTPase. For fast and accurate recognition of the appropriate tRNA, the ribosome utilizes large conformational changes (conformational proofreading). 
Now the P site contains the beginning of the peptide chain of the protein to be encoded and the A site has the next amino acid to be added to the peptide chain. The growing polypeptide connected to the tRNA in the P site is detached from the tRNA in the P site and a peptide bond is formed between the last amino acids of the polypeptide and the amino acid still attached to the tRNA in the A site. This process, known as peptide bond formation, is catalyzed by a ribozyme (the 23S ribosomal RNA in the 50S ribosomal subunit). Now, the A site has the newly formed peptide, while the P site has an uncharged tRNA (tRNA with no amino acids). The newly formed peptide in the A site tRNA is known as dipeptide and the whole assembly is called dipeptidyl-tRNA. The tRNA in the P site minus the amino acid is known to be deacylated. In the final stage of elongation, called translocation, the deacylated tRNA (in the P site) and the dipeptidyl-tRNA (in the A site) along with its corresponding codons move to the E and P sites, respectively, and a new codon moves into the A site. This process is catalyzed by elongation factor G (EF-G). The deacylated tRNA at the E site is released from the ribosome during the next A-site occupation by an aminoacyl-tRNA again facilitated by EF-Tu.
The ribosome continues to translate the remaining codons on the mRNA as more aminoacyl-tRNA bind to the A site, until the ribosome reaches a stop codon on mRNA(UAA, UGA, or UAG).
The translation machinery works relatively slowly compared to the enzyme systems that catalyze DNA replication. Proteins in bacteria are synthesized at a rate of only 18 amino acid residues per second, whereas bacterial replisomes synthesize DNA at a rate of 1000 nucleotides per second. This difference in rate reflects, in part, the difference between polymerizing four types of nucleotides to make nucleic acids and polymerizing 20 types of amino acids to make proteins. Testing and rejecting incorrect aminoacyl-tRNA molecules takes time and slows protein synthesis. In bacteria, translation initiation occurs as soon as the 5' end of an mRNA is synthesized, and translation and transcription are coupled. This is not possible in eukaryotes because transcription and translation are carried out in separate compartments of the cell (the nucleus and cytoplasm).