A 3.00 kg that is several hundred meters above the earth's surface 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 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) = 1.00 s and (ii) = 3.00 s? (b) What is the maximum distance that the box descends below its initial position? (c) At what value of f does the box return to its initial position