Ahorizontal rope is tied to a 50.0kg box on frictionless ice. what is the tension in the rope if,
a. the box is at rest
b. the box moves at a steady 5.0m/s
c. the box has v_x=5.0m/s and a_x=5.0m/s²

A horizontal rope is tied to a 50.0kg box on frictionless ice. 

A. the box is at rest; 
     zero acceleration ==> no net force on the box ==> no tension in the rope

B. the box moves at a steady 5.0m/s;
     zero acceleration ==> no net force on the box ==> no tension in the rope

C. the box has v_x=5.0m/s and a_x=5.0m/s²
     Finally some acceleration !     F = m A
     Net force on the box is (mass) x (acceleration)
                                         = (50 kg) x (5 m/s²)
                                         =        250 Newtons.

The only thing in the vicinity that can exert force on the box is the rope,
so the tension in the rope must be 250 N, and somebody or some thing
must be pulling on the other end in order to maintain the force and the
acceleration of the box.

Dis the