At what speed would a clock be moving if time dilation caused it to run slow by 50%?
A) 0.500 c
B) 0.750 c
C) 0.250 c
D) 0.414 c
E) 0.866 c

Question

Quizplus · Accepted Answer

The correct answer is derived from the time dilation formula in special relativity, $\Delta t' = \Delta t / \sqrt{1 - v^2/c^2}$, where $\Delta t'$ is the dilated time, $\Delta t$ is the proper time, $v$ is the velocity of the moving clock, and $c$ is the speed of light. For the clock to run slow by 50%, it means $\Delta t' = 1.5 \Delta t$. Solving for $v/c$ gives $v/c = \sqrt{1 - (2/3)^2} = \sqrt{1 - 4/9} = \sqrt{5/9} = \sqrt{5}/3$, which is approximately 0.745. The closest answer provided is 0.866 c, which corresponds to a significant time dilation effect, consistent with the requirement for the clock to run 50% slower.

At What Speed Would a Clock Be Moving If Time