A train of length λ = 350 m starts moving rectilinearly with constant acceleration ω = 3.0 ×10 –2 m/s 2 ; t = 30 s after the start the locomotive headlight is switched on (event 1), and τ = 60 sec after that event the train signal light is switched on (event 2). Find the distance between these events in the reference frames fixed to the train and to the Earth. How and at what constant velocity V relative to the Earth must a certain reference frame K move for the two events to occur in it at the same point?
Text Solution
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x 1 – x 2 = λ – w τ (t + τ /2) = 
km, Towards the train with velocity v = 4 m/s
Sol. In the frame of train, the distance between A and B remains constant which is equal to λ = 350. Hence, in the frame of train the distance between two events is equal to AB = λ = 350 m.
Distance between these points with respect to ground
d = λ + x 1 – x 2
= λ + 
ω t 2 – 
ω (t + τ ) 2
= λ – ωτ 
~ 240 m
Time between these two events = τ = 60 sec.
Velocity of frame V = 
= 4 m/s.
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