Psalm 46:1–2 was written for exactly the kind of sudden, destabilizing catastrophe a serious accident represents: "God is our refuge and strength, a very present help in trouble. Therefore will we not fear, though the earth be removed, and though the mountains be carried into the midst of the sea." The Hebrew mut — 'removed' — means to totter, to shake violently. A car accident is the earth being removed under you. The psalmist's confidence is not that the earth won't shake. It is that God is the refuge inside the shaking.
The Hebrew word shaqat — to be quiet, to rest, to settle — appears in Psalm 107:30 after a description of people in a storm at sea: "Then are they glad because they be quiet; so he bringeth them unto their desired haven." After the storm. After the violence. After the terror — God brings them to quiet. The nervous system's road back from traumatic shock is exactly this: the gradual finding of quiet after the storm. God is named as the one who brings people there.
Commentary is from a charismatic Protestant perspective, drawing on KJV text and public-domain sources including Spurgeon, Andrew Murray, and Matthew Henry.