I have a question on the pre-exam which I did not get.
Consider a spaceship that leaves Earth at event A and travels in the +x direction. It accelerates at a constant rate from rest at time t = 0 to a final speed of 4/5 at time t = 1 hour. It remains at that speed thereafter. Just as the spaceship reaches its final speed, it emits a laser signal back toward Earth, this is event B. The signal reaches Earth at event C.
(a) Show that the spacetime coordinates of event B are (t, x) = (1, 0.4) in hours.
Maybe someone can help me?
The problem is poorly stated because there are no units. However, if you use the implied units and the basic equations for velocity and distance with constant acceleration, the solution should be straightforward to someone who just spent a semester studying physics. I would suggest you go talk with your physics professor. You are probably making this problem much more difficult than it actually is.
As a hint, event C has no bearing on solving this problem.
The distance dx= x0+v0⋅t+0.5⋅a⋅t²
where:
x0: starting point
v0: starting speed
a: acceleration
t: time
The previous responses don't seem to consider relativity?!?! Anyhow, the wikipedia article on space time covers a very similar problem in the section on acceleration. https://en.wikipedia.org/wiki/Spacetime#Acceleration