Chapter 8.1, Problem 4P

Find the distance which an object moves in time $t$ if it starts from rest and has an acceleration $d^{2}x/d{t}^2=g{e}^{-kt}.$ Show that for small $t$ the result is approximately (1.10), and for very large $t$, the speed $dx/dt$ is approximately constant. The constant is called the terminal speed. (This problem corresponds roughly to the motion of a parachutist.)