Physics

Problem

16. An object is released from rest at time

\mathrm{t}=0

and falls through the air, which exerts a resistive force such that the acceleration a of the object is given by

\mathrm{a}=\mathrm{g}-\mathrm{bv}

, where v is the object's speed and b is a constant. If limiting cases for large and small values of

t

are considered, which of the following is a possible expression for the speed of the object as an explicit function of time? (A)

\mathrm{v}=\mathrm{g}\left(1-\mathrm{e}^{-\mathrm{bt}}\right) / \mathrm{b}

(B)

v=\left(g e^{b t}\right) / b

(C)

v=g t-b t^{2}

(D)

v=(g+a) t / b

(E)

v=v_{0}+g t, v_{0} \neq O

(A)

\mathrm{v}=\mathrm{g}\left(1-\mathrm{e}^{-\mathrm{bt}}\right) / \mathrm{b}

(B)

\mathrm{v}=\left(\mathrm{g} \mathrm{e}^{\mathrm{bt}}\right) / \mathrm{b}

(C)

\mathrm{v}=\mathrm{g} \mathrm{t}-\mathrm{b} \mathrm{t}^{2}

(D)

\mathrm{v}=(\mathrm{g}+\mathrm{a}) \mathrm{t} / \mathrm{b}

(E)

\mathrm{v}=\mathrm{v}_{0}+\mathrm{g} \mathrm{t}, \mathrm{v}_{0} \neq \mathrm{O}