A 3.00-kg box that is several hundred meters above the surface of the earth is suspended from the end of a short vertical rope of negligible mass. A time-dependent upward force is applied to the upper end of the rope, and this results in a tension in the rope of T(t) = (36.0 N/s)t. The box is at rest at t = 0. The only forces on the box are the tension in the rope and gravity.

(a) What is the velocity of the box at (i) t = 1.00 s and (ii) t = 3.00 s?

(b) What is the maximum distance that the box descends below its initial position?

(c) At what value of t does the box return to its initial position?