Time and speed question. ?

If I'm walking and a child steps in front of me I merely step around having plenty of time. If I'm driving eighty mph I panic and swerve having almost no time to react. if I'm traveling at the speed of light I need no time to react because the child appears to be standing still. What would my perception of time be if I were completely stopped in relation to the origin of the big bang rather than flying thru space with the stars and galaxies? How fast would I need to travel toward the center of the universe to become completely stopped in relation to it?