A train of length `l=350m` starts moving rectilinearly with constant acceleration `w=3.0*10^-2 m//s^2`, `t=30s` after the start the locomotive headlight is switched on (event 1), and `tau=60s` after that event the tail signal light is switched on (event 2). Find the distance between these events in the reference frames fixed to be 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

`350 m rarr` with respect to train; `242m`, with respect to Eargh;
`4.03 m s^(-1)`

Explanation

`S_(1)=(1)/(2)(3xx10^(-2))(30)^(2)=13.5 m`
`S_(2)= (1)/(2) (3xx10^(2)(90)^(2) =121.5 m`
`d=S_(2)-S_(1)=108 m`
.
a. `350 m rarr` with repect to train
`x=l-d=350-108 =242 m`, with respect to Earth
b. `v=(242)/(60) =4.03 ms^(-1)`.