The car speed cruise control Input-Output model is given by

\[\dot{v}+\frac{b}{m} v=\frac{b}{m} v_{r},\]

for a step input \(v_{r}(t)\). The car speed response was obtained by the direct time domain determination as

\[v(t)=v_{r}\left[1-e^{-\frac{b}{m} t}ight] .\]

Show that the Laplace transforms method produces the same result.