This is pretty easy.
Select the Long Island Rail Road -> Timetable -> M7 LIRR -> Any route you want. It picks up speed pretty quickly. I think I used route 2008.
Don't worry about loading passengers if you're just trying to get the speed achievement.
Set the master key to unlocked.
Set the reverser to forward.
Set the master controller to max brake.
Hold the charge brakes button (on the left wall panel) until the gauge is in the green.
Set the master controller to max power and then just let it go.
It should only take a couple of minutes to get up to 70mph. It took a little bit for mine to pop, so just let it run until you get it.