Plotting Minkowski diagram for 2 simultaneous accelerating

[aquaman]

Homework Statement

two objects are at rest in an inertial reference frame. Two objects accelerate simultaneously in the same direction until reaching half the velocity of light and then halt simultaneously. The two objects are initially connected by a thread just long enough to cover the distance between the two objects. The question is what will happen to the thread due to relativistic length contraction.

Draw a Minkowski diagram of the world lines of both objects.

Homework Equations

f is intertial reference frame. t=0 is initial state rest, T is ending rest state.

The Attempt at a Solution

I uploaded a really poor sketch of what I think would occur. The thread would remain intact because of reaching half the velocity of light wouldn't curve space time or force the two objects to separate enough.

I am taking a "philosophy of scientific thought" course and am a bit in over my head right now. Any help would be greatly appreciated.

Also, apologize if this version of the subject matter isn't part of this forums content.
Thanks.

 

[robphy]

What would the worldline of a uniformly accelerating observer look like?
How does one represent the instantaneous velocity of an observer on a spacetime diagram?

 

[Mister T]

You have to assume, for the sake of discussion, that half the speed of light produces a significant relativistic length contraction.

A vertical world line means that as time passes there is no change in position.

Start by drawing the world line of just one of the objects. As a primer, draw the world line of an object moving at a steady speed of half the velocity of light. Then realize what happens to the world line before that, and then after that.