A person standing on a platform notes that a train travelling with a velocity of 0.6c requires one second to pass by them. Determine the rest length of the train.

Step-by-step solution

The velocity of the train is v = 0.6c and the time taken to pass the observer is t = 1 s . The length of the train as measured by the observer on the platform is the contracted length L . L = v t = 0.6c 1 = 0.6 3 10^8 m = 1.8 10^8 m According to the length contraction formula, the relation between the contracted length L and the rest length L₀ is: L = L₀ 1 - v^2 c^2 L₀ = L 1 - v^2 c^2 Substituting the values of L and v : L₀ = 1.8 10^8 1 - (0.6)^2 L₀ = 1.8 10^8 1 - 0.36 L₀ = 1.8 10^8 0.8 L₀ = 2.25 10^8 m