Final answer:
The net change in kinetic energy of a cart moving from x = 0 m to x = 4 m on a level track with a force exerted parallel to the x-axis is an increase of 10 J.
Step-by-step explanation:
When considering the work-energy theorem, any work done on an object results in a change in its kinetic energy. The work is calculated as the force applied over a displacement and in the direction of that force. If a force is applied parallel to the displacement in a frictionless scenario, the entire force contributes to the work. When a cart is moving on a level track and experiences a force acting parallel to the x-axis, as the cart moves from x = 0 m to x = 4 m, the net work done by the force would be equal to the net change in kinetic energy of the cart.
Given the information provided, it can be deduced that if the work done by the spring on the carts results in 10 J of kinetic energy, and the force is applied in the direction of travel, the kinetic energy of the cart would increase. Therefore, between the provided choices, the correct answer is an increase of 10 J in the kinetic energy of the cart.