Peter asks for a sign that the "apparition" really is Jesus, and He replies, "Come!" His response contains an implicit pledge that Peter would not be engulfed in the raging waters. At first, Peter's confidence in Jesus' power sustains him as he walks on the water, but as doubt quickly creeps in, his enjoyment of the intensely spiritual experience soon fades.
Peter's zealous, impulsive faith is not absolute, convicted faith but humanly reasoned, self-assured, and immature, though it allowed him to attempt the seemingly impossible feat of walking on water. Jesus is gentle in His rebuke, not saying, "Why did you bother to come?" but gently asking, "O you of little faith, why did you doubt?" as He held out a hand to reassure Peter.
Despite his initial faith, Peter soon found himself facing a dramatic test. In the clash between sight and faith (II Corinthians 5:7), his impulsive faith vanished and fear took its place. Taking his eye off his Savior to focus on the raging waves, he sank but did not drown. Jesus saved him because He never abandons His elect. Poor Peter must have felt humiliation that night as his fear and failure revealed his weakness and lack of true faith.
Once Jesus entered the ship with Peter, the winds immediately ceased. Ceased in Matthew 14:32 means "to grow weary." The rough elements had spent themselves, having been overcome by supernatural power. In that instant, the ship was supernaturally and immediately moved to the shore.