A 2.60kg 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)=(38.0N/s)t . The box is at rest at t =0. The only forces on the box are the tension in the rope and gravity.
What is the velocity of the box at 1.00s ?
What is the velocity of the box at 3.00s ?
What is the maximum distance that the box descends below its initial position?
At what value of t does the box return to its initial position?