a)the box is at rest?
b)the box moves at steady Vsubx=5.00 m/s
c)The box vsubx = 5.00 and asubx = 4.20 ?
I assume the rope is pulling the box.
a) There is no pulling force acting on the box, so T = 0
b) Since the motion is uniform and frictionless, there is still no force acting on the box, so again T = 0
c) There is a pulling force which causes the acceleration.
According to Newton’s law
T = ma = 54.0 x 4.20 = 227 N