Chapter 8.4, Problem 25ES

(a) Use the method of integrating factors to derive solution (16) to the initial-value problem (14). [Note: Keep in mind that c, m, and g are constants.]

(b) Show that (16) can be expressed in terms of the terminal speed (18) as

$\upsilon (t)=e^{-gt/{\upsilon }_T}({\upsilon }_0+{\upsilon }_T)-{\upsilon }_T$

(c) Show that if $s(0)=s_0,$ then the position function of the object can be expressed as

$s(t)=s_0-{\upsilon }_{T}t+\frac{{\upsilon }_T}{g}({\upsilon }_0+{\upsilon }_T)(1-e^{-gt/{\upsilon }_T})$