Answer:
Speed = 0.866c
Where c is speed of light
Step-by-step explanation:
We want to find the speed at which it run at a rate that is one-half the rate of a clock at rest.
Thus, we will use time dilation equation to solve it.
Thus;
t_o/√[1 - (v²/c²)] = 2t_o
Where:
t_o is time at rest
v is the speed at which it runs
c is the speed of light.
t_o will cancel out to give;
1/√[1 - (v²/c²)] = 2
Rearranging, we have;
√[1 - (v²/c²)] = ½
Let's make v the subject of the formula;
Let's square both sides to get;
1 - (v²/c²) = ½²
1 - (v²/c²) = ¼
Rearrange to get;
1 - ¼ = v²/c²
¾ = v²/c²
Take square root of both sides to get;
v/c = √¾
v = c × 0.866
v = 0.866c