0.975C or 0.975 of the speed of light=0.975(3*10^8m/s)=2.925*10^8m/s=v
Δt=Δt₀/(√1-v²/c²)⇒since you are traveling in space which has a different time frame than on earth and Δt is time measured by an observer in a different reference frame, you will be solving for proper time or Δt₀ which is the measured in the same reference frame as the events are actually occurring at. with some algebra we get ⇒Δt₀=Δt(√1-v²/c²).
We want our answer to be in breaths per minute so since velocity and speed of light are in both in m/s and the answer we want is to be in breaths/min, we won't change anything about the 8 breaths/min, no need to convert it to breaths/second.
Δt₀=8 breaths/min (√1-((2.925*10^8m/s)^2)/((3*10^8m/s)^2))))
Δt₀=1.8 breaths/min
