Distance between two events w.r.t. two frames

[Pushoam]

Homework Statement

Homework Equations

The Attempt at a Solution

Distance between events w.r.t. Earth frame,

D_e = | (1/2)w(t+Γ)² - 350 - (1/2)wt² | = 242 m

Distance between events w.r.t. train frame,
D_t =350 m , correct?
As w.r.t. train frame , the train is not moving.

But, a person on the train will observe that the train is accelerating.
But , if the train is not moving, then how will this person observe that the train is accelerating. Here , I am doing some mistake. Please help me.W.r.t. Earth's frame, the two events occur at (x₁,t₁) and (x₂,t₂)
such that x₁ - x₂= 242 m
and t₂ - t₁ = 60 s

At t = 0 s, origin of both K's and Earth's frames meet each other.
W.r.t. K's frame, the two events occur at (x'₁,t₁) and (x'₂,t₂)
such that x'₁ - x'₂= 0 m
and t₂ - t₁ = 60 s
x'₁ - x'₂= 0 m = x₁ - Vt₁ - x₂ + Vt₂

x₁ - x₂ = - V( t₂ - t₁ )

V = 242/60 = 4.0 m/s

 

[Orodruin]

But, a person on the train will observe that the train is accelerating.

No it will not. The train frame is a non-inertial frame.

 

[Pushoam]

No it will not. The train frame is a non-inertial frame.

How can I,too, reach to this conclusion?
If a person sitting in an accelerating train wants to measure the acceleration of the train, won't he measure the acceleration to be nonzero?

 

[Pushoam]

No it will not. The train frame is a non-inertial frame.

How can I,too, reach to this conclusion?
If a person sitting in an accelerating train wants to measure the acceleration of the train, won't he measure the acceleration to be nonzero?

 

[Orodruin]

How can I,too, reach to this conclusion?
If a person sitting in an accelerating train wants to measure the acceleration of the train, won't he measure the acceleration to be nonzero?

This depends on what you mean by "measuring the acceleration". An accelerometer will give you a non-zero value, but it will read the same in all frames. By definition of the train frame, the train is stationary in that frame and therefore not accelerating.

 

[Pushoam]

An accelerometer will give you a non-zero value, but it will read the same in all frames.

Does "all" imply both inertial and non-inertial frames?

By definition of the train frame, the train is stationary in that frame and therefore not accelerating.

So, we reach to that conclusion by definition.