Is there some other formula ... which ... does not allow the speed ... to surpass the speed of light?
That would be the equations of special relativity mentioned by sahinsahin in a comment.
Image from Loodog?
Another factor you have to take into account with classical mechanics is to work out how a constant force can be applied to your object over 11 months and 11 days without affecting it's mass (therefore no fuel onboard) and without the additional speed giving rise to large opposing forces such as friction.