I need help with an application of differential equation

Question

A body weighing 160 Ib is dropped 2000 ft above ground with no initial velocity. As it falls, the body

encounters a force due to air resistance proportional to its velocity. If the limiting velocity of this body is 320 ft/sec, find (a) an expression for the velocity of the body at any time t and (b) an expression for the position of the body at any time t.

please write the solution with full steps

Answer 1

(a) As they have given the limiting velocity i.e. the terminal velocity then we have to find the time it take for the body to reach terminal velocity and then in the expression for velocity you give velocity in two different time intervals.

(b) Here you have act like the object was accelerating till it reaches its terminal velocity and then it moves at constant speed. Use this to solve the question.