A space probe of mass \(m\) coasts in deep space with an initial velocity \(v_0\,\hat{\imath}\). At time \(t = 0\), a braking thruster activates, exerting a net external force \(\vec{F}(t) = -F_0 e^{-t/\tau}\,\hat{\imath}\) along the line of motion, where \(F_0\) and \(\tau\) are positive constants. In the limit \(t \to \infty\), which of the following statements correctly describes the motion and velocity of the probe?