Suppose that you are traveling on board a spacecraft that is moving with respect to the earth at a speed of 0.975c. you are breathing at a rate of 8.0 breaths per minute. as monitored on earth, what is your breathing rate?

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