At what speed would a clock have to be moving in order to run at a rate that is one-fourth the rate of a clock at rest?
A)0.87c
B)0.75c
C)0.97c
D)0.50c
E)0.26c

Question

At what speed would a clock have to be moving in order to run at a rate that is one-fourth the rate of a clock at rest?
A)0.87c
B)0.75c
C)0.97​c​
D)0.50c
E)​0.26c

Quizplus · Accepted Answer

According to the theory of relativity, time dilation is given by the formula $ t' = t/\sqrt{1-v^2/c^2} $. For the moving clock to run at one-fourth the rate of the clock at rest, $ t' = 4t $. Solving $ 4 = 1/\sqrt{1-v^2/c^2} $ gives $ v = 0.97c $.

At What Speed Would a Clock Have to Be Moving