Final answer:
No provided force option (1 N, 19 N, 39 N) will allow the object to maintain constant velocity, as none of these equate to the necessary 20 N force in the opposite direction to balance the existing forces.
Step-by-step explanation:
The question concerns the topic of Newton's First Law of Motion, specifically the condition of dynamic equilibrium where an object moves with constant velocity, implying that the net force acting on it is zero. In this scenario, three forces of magnitudes 5 N, 15 N, and 20 N are already acting on an object. To maintain a constant velocity, the net force must remain zero; therefore, any additional force must balance out these existing forces.
Since the forces of 5 N and 15 N can be assumed to cancel each other out due to their opposing directions (assumption based on the fact of constant velocity), the effective force to balance would be 20 N. Thus, the additional force needed to keep the object moving at constant velocity would also need to be 20 N but in the opposite direction to the existing 20 N force. The options provided in the question do not include a 20 N force, so none of the provided options (1 N, 19 N, 39 N) are correct.
Therefore, the correct answer is that none of the forces listed can act on the object to maintain a constant velocity. Had there been an option for a 20 N force in the opposite direction to the existing 20 N force, that would have been the correct choice.