Wayne, you said to use 1/200 and normal flash. Now that I have the YN568, I am a little confused on that setting. The only way I could get the ISO to adjust in the A-priority, was to use i-ttl mode. In that mode the camera metering system will detect flash illumination back from the object and automatically control the flash output. That sounds simple, but the max of the zoom range lamp holder is 105 mm--(not sure what that means). The person that was going to get the YN568EX on loan to me did not work out, so I purchased my own.
Is this indoor flash, or fill in sunlight? And which camera model? (makes a really big difference about Auto ISO action with flash). Bounce flash?
Fill flash outdoors in sun, then Auto FP mode could possibly be an option, allowing any shutter speed, but with rather limited power range. A different subject.
Indoors is my assumption, you said "at work".
In camera A mode, the only way to get a fast shutter speed is to go out into bright ambient, where it will meter high. But there are other plans. More in bold below, but first, why?
Indoors with flash, typically we ignore the ambient, and use low ISO to make ambient be minimal (because incandescent is orange, and fluorescent can be green... but flash is white, and mixing light sources is a terrible plan). And high ISO makes seeing ambient be worse.
The camera meter and reading and settings that we see are NOT about the flash. It is about the ambient, which typically for indoors flash, we don't care about. The camera automation sets up for the ambient, NOT for the flash. But the poor old flash has to use whatever ISO and whatever aperture it discovers is in effect at its time. However, we can plan both ISO and aperture for the flash.
For this example, with flash turned off.... Say set ISO 400 for bounce, and in A mode, set say f/5 for bounce (but flash is still turned off).
Indoors, camera A mode, maybe this shutter speed says 1/15 second (dim indoors, and flash will help it). Value is guessed, not important, point is, shutter is slow in dim light (dimmer than sunlight).
Reach up and turn on the flash, and camera A mode will jump to 1/60 second (Minimum Shutter Speed With Flash, menu E2). (Slow Sync or Rear Curtain Sync are exceptions, shutter speed will not jump up).
This is not a metering, it is a Minimum shutter speed, because we are using flash instead, and we don't need it slower. So this jump underexposes ambient, which is good (hides bad color) and we don't care, we are using flash instead. But 1/60 can let a little of it through anyway.
Maybe better, indoors (insignificant ambient),
use camera M mode (camera is manual, we can set 1/200 f/5 ISO 100) ... but
TTL flash is still automatic flash in any camera mode. Then we can set 1/200 or 1/250 second (maximum sync speed), for the purpose to keep the colored ambient light out.
Any studio situation would do exactly this, low ISO, and up around 1/200 second shutter. If the flash were turned off, then we hopefully see a black picture, no ambient. Shutter speed affects and underexposes ambient, but shutter speed does not affect flash exposure (shutter just has to be open to let the fast flash through). For many camera models, Auto ISO won't allow low ISO indoors, so turn it off with flash. For direct flash, this underexposure of ambient makes the far room dark (you may need a light on the background), but if bounce flash, it probably lights any normal size room anyway, adequately, probably.
I'm not sure if this was the question? See
Four Flash Photography Basics we must know - Flash pictures are Double Exposures for more.