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Kinematics

Problem 1.14

A train of length \(l=350 \mathrm{~m}\) starts moving rectilinearly with constant acceleration \(w=3.0 \cdot 10^{-2} \mathrm{~m} / \mathrm{s}^{2} ; t=30 \mathrm{~s}\) after the start the locomotive headlight is switched on (event \(l\) ), and \(\tau=60 \mathrm{~s}\) 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?

Reveal Answer
x1−x2=l−wτ(t+τ/2)=0.24 km. Toward the train with velocity V=4.0 m/sx_{1}-x_{2}=l-w \tau(t+\tau / 2)=0.24 \mathrm{~km} . \text { Toward the train with velocity } V=4.0 \mathrm{~m} / \mathrm{s}
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