Explain what is meant by terminal velocity and determine its value in this case.

Show that the mass hits the ground after a time T given by

T = (kh/mg) + (m/k)(1-exp(-kT/m))

Assumig that k << m and by expanding the right hand side in powers of k/m up to order (k/m)^2, obtain an expression for T which is correct up to and including terms of order k/m.

I've managed to get an equation of motion and a terminal velocity, but I can't derive that middle equation. HELP!