Final answer:
The object acted upon by a net force F in the +x direction for 1 second will continue to move with a constant velocity only in that direction after the force stops acting. Therefore, after 3 seconds, the object's velocity vector can only have an x-component, making (a) 3Fi^ the correct choice, representing the velocity in the +x direction.
Step-by-step explanation:
Given that an object of mass m is initially at rest and free to move without friction in the xy-plane, and a constant net force F directed in the +x direction acts on the object for 1s, we use Newton's second law of motion, which can be represented as Fnet = ma, to determine the object's motion. Since the force is applied in the +x direction, the object will only accelerate in that direction, and there will be no acceleration in the y-direction because no force is applied there.
After 1 second, the object will have a velocity in the +x direction due to the force F. The magnitude of this velocity vector can be calculated using the formula v = u + at, where u is the initial velocity (0 m/s), a is the acceleration (F/m), and t is the time (1s). Since after 1 second, there are no more forces acting on the object, it will continue to move with the constant velocity it gained during the first second, which means no additional y-component will be added. Therefore, the correct answer must only have a component in the x-direction.
Among the provided options, the only velocity vector with no y-component is (a) 3Fi^, which indicates the object will be moving with a velocity in the +x direction after 3 seconds with no additional motion in the y-direction.