Final answer:
The question pertains to calculating a relativistic velocity (u), given velocities are fractions of the speed of light (c). The problem seems to require the use of the relativistic addition of velocities formula. However, without the actual equation modeled or further context, we cannot properly solve for u.
Step-by-step explanation:
The question seems to be related to Einstein's theory of special relativity, particularly involving the addition of velocities. The knowns given, v=0.500c and u' = c or u' = 0.750c, suggest that the scenario involves velocities that are fractions of the speed of light (c). We need to apply the equation for relativistic velocity addition to find the unknown velocity (u).
The equation for the relativistic addition of velocities is:
u = (u' + v) / (1 + (u'v/c²))
Plugging the knowns into this equation will allow us to solve for the unknown u. In case the question refers to a simplified scenario or a different context, we might need a different equation to solve for velocity. However, without the full context or the actual equation modeled, it is not possible to provide the solution.