Two protons placed near one another with no other objects close by would a) accelerate away from each other. b) remain motionless. c) accelerate toward each other. d) be pulled together at constant speed. e) move away from each other at constant speed.

In this situation, the only significant force acting on the protons is the electrostatic force. According to Coulomb's Law, this force can be calculated using the formula: F = k * (q1 * q2) / r^2 where F is the force, k is the electrostatic constant, q1 and q2 are the charges of the protons, and r is the distance between them. Since both protons have the same positive charge, this force will be repulsive.

Since the electrostatic force is repulsive and is the only force acting on the protons, they will experience an acceleration away from each other due to this force. Newton's second law states that: F = m * a where F is the force, m is the mass of the particle, and a is its acceleration. In this case, the repulsive force between the protons will cause them to accelerate away from each other. Now, let's analyze each option given in the exercise: a) accelerate away from each other: This is the correct answer based on our understanding of Coulomb's Law and Newton's second law. b) remain motionless: This is incorrect because the repulsive force between the protons will cause them to accelerate away from each other. c) accelerate toward each other: This is incorrect because the electrostatic force between the protons is repulsive, not attractive. d) be pulled together at constant speed: This is incorrect because the force between the protons is repulsive, not attractive. e) move away from each other at constant speed: This is incorrect because the protons will experience acceleration due to the repulsive electrostatic force and will not move at a constant speed. Therefore, the correct answer is option a) accelerate away from each other.