Its impossible for the particle to move 8 meters from the starting position at 2 seconds. sqr root (3t-1) anything below time 1/3 is a negative sqr root number. between time 1/3 and 2 the distance traveled in 2.48 meters. At time 2 it is sqr root (5), at time 1 it is sqr root (2), at time 1/3 it is 0 this doesn't even come close to 8 meters. If a constant is added to the anti derivative what that will mean is the starting position doesn't happen at 0.