Typically you can use any shutter speed slower than the upper limit,
1/60th sounds about right as the upper limit.

1/60 sec or slower is correct if your camera has a focal plane shutter.  But
your Yashica A - like all TLRs - has a leaf shutter.  So just make sure you
have the camera at X-synch and fire away at any and all speeds with your
Sunpak electronic flash.  It is easy enough to test - put a roll in the
camera, set the synch to X, and fire away varying the shutter speed....no
exposure compensation using the f/stop.  The different shutter speeds have
no effect on exposure when ambient light is low/non existent...exposure is
controlled by f/stop/subject distance as indicated by info on your flash.

I don't know the Yashica A, but for most horizontal focal plane shutters,
1/60 is maximum. If the pictures have one side cut off, then it's longer
than 1/60. If it's a between-the-lens shutter, just about any speed is good.
(The preceding is a _general_ statement that applies to many 35mm cameras,
and possibly MF cameras.)
Is this a MF twin lens reflex? if so, try
http://www.butkus.org/chinon/yashica/yashica_a/yashica_a-splash.htm. For
many camera instruction books, try the first part of that
URL--http://www.butkus.org/

Thanks all.  I used a Yashica A with an older flash unit and then a Sunpak
555 when they were introduced to take many accident scene photographs up
until 1983 when the department switched to 35 mm.  

Our Physical Evidence Section also used them and they were excellent for
both black and white and color photographs, especially when enlarged for
court presentation.

I can only imagine now they have gone to digital which at first caused many
court battles over the admissibility of the photos as evidence due to the
very simple procedure to alter them.

An antique camera for an antigue operator------------

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You're not incorrect with 1/60th, but Yashica A cameras have leaf
shutters so you should be good to go as fast as the lens shutter will go.

You can use any shutter speed, up to the camera's maximum speed of 1/300 of
a second.

The Yashica-A was my first camera, which I was given at age 9, along with a
Sekonic "Brockway" exposure meter.

It has been awhile since I used it, and I do not recall if there was an "X"
synchronization setting.  The camera came out circa 1958.  Were there any
electronic flash units available then?  I don't think I ever used a flash
unit with my camera--all my shots with it were taken in daylight.

The irony of this is that, even after I migrated to 35mm photography, I
typically used the 50mm normal lens for about 90 percent of my work (I shoot
landscapes, street scenes and buildings that are about to be demolished--my
little way of preserving the past).  The 80mm normal lens on the "A" might
have been an impediment to some, but I could have gotten by with that camera
and lens for decades, and would have been quite happy with the results.
Even that non-coated lens yields more image quality than the best 35mm,
because of the greater film size.

It might not be the best choice for action photos, where automatic exposure
and faster film advance are real advantages, but for more static subjects it
remains a fine piece of equipment.  Enjoy it!