E1: Start the simulation and check when relativistic effect become noticable. Try this for different accelerations.

E2: Observe the light cone originating from the moving object. How will the observer at rest appraise light signals emitted forward or backward?

E3: Reflect about the scaling of "earthly" happenings. Take as an example a rocket with constant acceleration of 10 times that of earthly gravitation g  = 9,8 m/s2. How long will it take till relativistic effects become noticeable? How far away will the object be at that time?

E4: Hint for E3: The graphic shows that relativistic effects are manifest above 1/2 c. Calculate t classically for that limit with v = bt.  Then s  = b/2 t.2

E5: The time resulting will not be extreme. What is the real limiting resource? Do some calculation!