This applet plots the velocity of a uniformly accelerated body, as seen from an inertial frame of reference. The local acceleration, that is, the acceleration perceived by the travellers, can be edited with the control bar.
As can easily be seen, the velocity approaches asintotically to the speed of light. That is, the acceleration appears to cease as seen from the inertial frame, but its still constant in the moving one.
The time appears to run slower in the moving frame as seen from the inertial one.
Also, the classical results for the same problem can be plotted in order to compare the differences.