{"knowledge_schema": {"broad_category": "Physics \u2192 Relativity \u2192 Particle Dynamics", "refinement": "This problem involves the relationship between rest mass energy, total energy, and velocity of a particle in the context of special relativity.", "specific_scope": "The focus is on calculating the velocity of a particle given its rest mass energy and total energy, using the principles of relativistic energy equations.", "goal": "Determine the velocity of the particle as a fraction of the speed of light (c) based on the provided energy values."}, "summary": "This problem is rooted in the principles of special relativity, specifically relating rest mass energy and total energy to the velocity of a particle. Given the rest mass energy of 200 GeV and total energy of 500 GeV, the task is to calculate the particle's velocity as a fraction of the speed of light. By applying the relativistic energy equation, we can derive the velocity, which in this case is found to be 0.9c."}