Can an object exceed the speed of light if we push it for enough time?

The second Newton's law of motion establishes that, in an inertial reference frame, the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object. That means that if we apply a constant force on a body without friction, then the object will move with constant acceleration, increasing its speed by the same amount every second.
The acceleration is proportional to the force, so if the net force is 100 Newtons and the mass is 2 kilograms, the acceleration will be 50 meters per second every second. But if the force is 2 N, the body will increase its speed by 1 m/s every second. Notice that this is not a huge acceleration. Nevertheless, if we keep pushing and wait for 300000000 seconds (9.5 years) the object will move faster that light.

But we know that nothing can exceed the speed of light. This is a well-established law of nature whose confirmation has become routine in current particle accelerators.

Try to find the solution to this contradiction!

Please, explain your reasoning. You can post your attempted answers in the comment box below. Please, do not use Facebook or Twitter to give your answers.

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