People hoping to travel to other worlds are faced with huge challenges. one of the biggest is the time required for a journey. the nearest star is 4.1×1016m away. suppose you had a spacecraft that could accelerate at 1.0 g for two thirds of a year, then continue at a constant speed. (this is far beyond what can be achieved with any known technology.)

I think the question here is about the initial velocity. If it is, then the working equation to be used is:

x = vt + 0.5at²
where
x is the distance
v is the velocity
t is the time
a is the acceleration

The acceleration due to gravity is 1.0g or 1.0(9.81 m/s²) = 9.81 m/s². There are approximately 3.154×10⁷ seconds in a year.

4.1×10¹⁶ m = v(2/3 yr * 3.154×10⁷ s/yr) + 0.5(9.81 m/s²)(2/3 yr * 3.154×10⁷ s/yr)²
Solving for v,
v = 1,846,769,088 m/s