# Work done on object in space

Suppose we apply a force of 1N on an object in space,due to Newton's 1st law of motion it should go on forever,therefore it's displacement goes on increasing.Does that mean that work done is infinite,as work is product of force and displacement.I can't wrap my head around it??please clear my doubt

In the case of no forces but $$\vec{v} \neq \vec 0$$, the work is zero since there is displacement but there is no force so the product vanishes.