Power Physics

The 100 kg box shown below is being pulled along the x-axis by a student. The box slides across a rough surface, and its position \(x\) varies with time \(t\) according to the equation \(x = 0.5t^3 + 2t\) , where \(x\) is in meters and \(t\) is in seconds.



A. Determine the speed of the box at time \(t\) = 0.

B. Determine the following as functions of time \(t\).

i. The kinetic energy of the box

ii. The net force acting on the box

iii. The power being delivered to the box

C. Calculate the net work done on the box in the interval \(t\) = 0 to \(t\) = 2 s would be greater than, less than, or equal to the answer in part (C). Justify your answer.