A body of mass 10 slugs is dropped from a height of 1000ft with no initial velocity. The body encounters an air resistance proportional to its velocity. If the limiting velocity is known to be 320ft/s, find an expression for the velocity of the body at any time t, an expression for the position of the body at any time t, and the time required for the body to attain a velocity of 160ft/s.

Question

A body of mass 10 slugs is dropped from a height of 1000ft with no initial velocity.  The body encounters an air resistance proportional to its velocity.  If the limiting velocity is known to be 320ft/s, find an expression for the velocity of the body at any time t, an expression for the position of the body at any time t, and the time required for the body to attain a velocity of 160ft/s.