Final answer:
The potential energy of a particle due to a constant horizontal force of 10 N directed towards a wall is given by U = 10x, when the potential energy at the wall is zero, making the correct answer A. U = 10x.
Step-by-step explanation:
The student has been given a scenario where a constant force of 10 N is acting horizontally on objects, directed towards a wall. To find out the potential energy (U) of a particle at a distance x from the wall, we use the concept of work done by a constant force, which is given by the formula Work = Force × Distance. Since the potential energy at the wall is considered to be zero, the potential energy at some distance x from the wall would simply be the work done by the force over that distance. Consequently, U = 10x because when the particle is moved against the direction of the force towards the wall, the force does positive work on it, thus increasing its potential energy by an amount Force × Distance. Hence, the correct answer is A. U = 10x.