An object of mass m falls from rest, starting at a point near the earth’s surface. Assum...

An object of mass m falls from rest, starting at a point near the earth’s surface. Assuming that the air resistance varies as the square of the velocity of the object, a simple application of Newton’s second law yields the initial-value problem for the velocity, v(t), of the object at time t :

where k, m, g are positive constants.

(a) Solve the foregoing initial-value problem for v in terms of t .

(b) Does the velocity of the object increase indefinitely? Justify.

(c) Determine the position of the object at time t .