With what speed will a clock have to be moving in order to run at a rate that is one-half the rate of a clock at rest

Speed = 0.866c

Where c is speed of light

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