Final answer:
The final speed of the car will increase by the square root of 2 when the force is applied over 80 m instead of 40 m, based on the work-energy theorem and assuming constant mass and no frictional forces.
Step-by-step explanation:
The question asks about the final speed of a car when a constant force is applied over different distances. Using the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy, we can solve this problem. Assuming the car's mass remains constant and ignoring any friction and air resistance, the work done on the car (force multiplied by distance) when the force is applied for 40 m translates into a certain amount of kinetic energy, which gives the car a final speed of 50 km/h.
If the same force is applied over 80 m, the work done (and thus the kinetic energy) will be double that of the 40 m case, because the distance is doubled while force is constant. As kinetic energy is proportional to the square of the speed (KE = 1/2 m v2), we can expect that the final speed will increase by a factor that is the square root of 2 (approximately 1.414).