Question

A train of length l = 350 m starts moving rectilinearly with constant acceleration w = 3.0x10^-2 m/s²; t = 30 s after the start the locomotive headlight is switched on (event 1) , and τ= 60 s after that event the tail 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?

Answer 1

In the reference frame fixed to the train, the distance between the two events is obviously equal to l. Suppose the train starts moving at time t=0 in the positive x-direction and take the origin (x=0) at the head - light of the train at t=0. Then the coordinate of first event in the earth's frame is

For the two events to occur at the same point in the reference frame K, moving with constant velocity V relative to the earth, the distance travelled by the frame in the time interval T must be equal to the above distance.

The frame K must clearly be moving in a direction opposite to the train so that if (for example) the origin of the frame coincides with the point x₁ on the earth at time t, it coincides with the point x₂ at time t+τ.