At what speed would a clock have to be moving in order to run at a rate that is one-third the rate of a clock at rest?
A)0.79 c
B)0.89 c
C)0.94 c
D)0.97 c

Question

Quizplus · Accepted Answer

According to time dilation, the rate of time on a moving object relative to a stationary object is given by the equation:
t' = t / sqrt(1-v^2/c^2)
where t is the time on the stationary clock, t' is the time on the moving clock, v is the velocity of the moving clock, and c is the speed of light.
If the moving clock is running at one-third the rate of the stationary clock, then t' = (1/3)t. Plugging these values into the time dilation equation and solving for v, we get:
1/3 = 1 / sqrt(1-v^2/c^2)
v^2/c^2 = 0.9444
v/c = sqrt(0.9444) = 0.971
So, the clock would have to be moving at a speed of 0.971c (rounded to two decimal places). The closest answer choice is option C, which is 0.94c.

At What Speed Would a Clock Have to Be Moving