A person travels by a car at a speed of 180 km h ⁻¹ . By his wristwatch, the journey from station X to station Y takes exactly 10 hours . What is the rest distance between the two stations?

Step-by-step solution

Speed of the car, v = 180 km h ⁻¹ = 180 5 18 m s ⁻¹ = 50 m s ⁻¹ . Time measured by the wristwatch of the person in the car is the proper time, t₀ = 10 h . Distance measured in the car's frame is L = v t₀ = 180 km h ⁻¹ 10 h = 1800 km . The rest distance between the two stations is the proper length L₀ . In the car's frame, the distance between the stations appears contracted, so L = L₀ 1 - v^2 c^2 . Therefore, L₀ = L 1 - v^2 c^2 . Using the binomial expansion for v c : L₀ L (1 + v^2 2c^2 ) = L + L v^2 2c^2 The addit