Re: how do u represent a reverse in velocity in the space time diagram?

Hello Hoda,

Space-time diagrams are not a complicated relativity thing.  They're
ordinary plots of "where did he go and when did he get there" ... and it
just so happens that the choice of axes makes some relativistic thought
easier.

Anyway, here we have time on the vertical axis and distance on the
horizontal. So travelling with 0.5 c means that I go to the right (along
the horizontal axis) at one-half unit of space for every one unit of time.
It's really just a line which travels right .5cm for every 1cm up.
To reverse direction ... there's nothing complicated and relativistic, you
are now going BACKWARDS 0.5 cm for every 1 cm up.

You'll get a correct world-line in this case if you IGNORE relativity and
plot, for example, the position-versus-time for a car that drives east for
10 minutes, then quickly reverses and drives west at the same speed.
Think about where you are at what times, plot the points, and you should
have your diagram.

I'm not going to do the transformations for you, since this sounds like a
homework problem.  Not sure what you did wrong on the Lorentz
transformation - I can't tell without seeing your calculations.

Hope this helps,

-Ben