Final answer:
The student's question involves the coefficient of restitution in a collision between two identical balls in physics, but lacks necessary information to determine the exact value of the coefficient for the given velocity conditions. none of the options are correct.
Step-by-step explanation:
The question concerns a collision between two identical balls, one of which is stationary before the collision. In physics, the coefficient of restitution (c) is a key factor in determining the outcome of such a collision. The coefficient of restitution is a dimensionless number between 0 and 1 that describes how energetic the collision is: a perfectly elastic collision has a c of 1, while a perfectly inelastic collision has a c of 0.
However, the question does not provide sufficient information to determine for what exact value of the coefficient of restitution the velocity of the balls after the collision would be two times the values of 0.5, 0.6, 0.7, or 0.8. Additional information regarding the system's initial conditions, such as the velocity of the first ball before collision, would be required to accurately answer this question.