An object of mass \( m \) is moving horizontally in a region where there is a resistive force \( F_{R}=-k v \), where \( k \) is a positive constant with units of \( \mathrm{N} \cdot \mathrm{s} / \mathrm{m} \) and \( v \) is in \( \mathrm{m} / \mathrm{s} \). The gravitational force exerted on this object is negligible. At time \( t=0 \) the object has an initial velocity \( v=v_{0} \). What is the expression for \( v \) as a function of time \( t \), where \( t \) has units of seconds?
(A) \( v_{0} e^{\frac{-k}{m} t} \)
(B) \( v_{0}\left(1-e^{\frac{-k}{m} t}\right) \)
(C) \( v_{0}\left(1-\frac{k}{m} t\right) \)
(D) \( v_{0}\left(1+\frac{k}{m} t\right) \)