AP PROBLEM FALLING MASS

A small body of mass M located near the Earth's surface falls from rest in the Earth's gravitational field. Acting on the body is a resistive force of magnitude KMV, where K is a constant and V is the speed of the body.

A. Draw and identify all of the forces acting on the body as it falls.

B. Write the differential equation that represents Newton's second law for this situation.

C. Determine the terminal speed for Vt of the body.

D. Integrate the differential equation once to obtain an expression for the speed V as a function of time T. Use the condition that V= 0 when T = 0.

E. Draw a graph of the speed V as a function of time T.