Question

With what velocity (relative to the reference frame K) did the clock move, if during the time interval `t=5.0s`, measured by the clock of the frame K, it becomes slow by `Deltat=0.10s`?

Answer 1

Because of time dilation, a moving clock reads less time. We write,
`t-Deltat=tsqrt(1-beta^2)`, `beta=v/c`
Thus, `1-(2Deltat)/(t)+((Deltat)/(t))^2=1-beta^2`
or, `v=csqrt((Deltat)/(t)(2-(Deltat)/(t)))`