The correctness of attributing of the improvement in speed of travel between 1800 and 1830 to railroads is dubious. This shows the extent of common carrier rail lines in 1835:
That's 1850. Between 1800 & 1830 much of the Southeast was still Native American nations, e.g. the portion of Alabama between Montgomery and the Georgia was the last part of the Creek Nation ceded in 1832.
The Federal and National Roads allowed stage travel, and that's what improved speed...for those who weren't walking. By 1850, other than the Seminoles, the Native American nations in the East had been conquered and rail road motive power had advanced.
The first railroad companies, with total individual rights of way typically of 10-30 miles, were just starting to get organized and begin operations in 1830. It wasn't for another 10-20 years that significant contiguous trackage existed. The world was very different in 1850 than it was in 1830.
http://en.wikipedia.org/wiki/File:USRail1835.jpg
What improved travel was the National Road, the Federal Roads, and the Military Road.
http://en.wikipedia.org/wiki/National_Road_%28United_States%...
http://en.wikipedia.org/wiki/Federal_Road_%28Cherokee_lands%...
http://en.wikipedia.org/wiki/Federal_Road_%28Creek_lands%29
http://en.wikipedia.org/wiki/Jackson%27s_Military_Road