A clock mechanism at rest has a period of exactly 1 second. When this clock is observed while moving with a speed of 0.80 c, what is its period?

1.67 s

Explanation:

Since the clock is moving at relativistic speed, the period dilates. So, we use the equation

t = t₀/√[1 - (v/c)²].

Given that t = the period of the clock = 1 s and v = speed of the clock = 0.80c, substituting these values into t, we have

t = t₀/√[1 - (v/c)²]

t = 1/√[1 - (0.8c/c)²]

t = 1/√[1 - (0.8)²]

t = 1/√[1 - 0.64]

t = 1/√0.36

t = 1/0.6

t = 1.67 s

So the period of the clock when it is observed while moving with a speed of 0.8c is 1.67 s