a broken , loose ,or missing tranny mount or perhaps UV joints going bad.
Only when accelerating, I would suspect a broken motor mount or bad CV joint.
Could be in need of a tune up.
Either your front end or your tires needs to be aligned.
Normally a bent wheel or tire out of balance.
By safe shutter, speed I assume you are wanting to know the slowest shutter speed that will not capture noticeable camera shake? There is no absolute answer to this. How much do your hands shake? The 'rule of thumb' I have used is 1/{focal length}. For a 400mm lens you would need a 1/400 sec or to use a tripod to avoid noticeable camera shake. For the 18mm you might get away with 1/20 or so. Although I despise using tripods, they will always give a sharper picture. You might need a microscope to tell, but you can tell.
Getting your tires balanced should help stop your shutter and shake.
The transmission is not shifting in and out of gear or your front joint is going bad
split axel they say on take off
Your front, left or right axle needs to be replaced.
There are several things that can cause your 1995 Chevrolet Blazer to shake when accelerating. Bad spark plugs and spark plug wires can cause the vehicle to shake. Tuning up the engine may eliminate the problem.
If your car shakes while accelerating check your motor mounts. Then check your transmission.
The tires may need alignment if it pulls to one side and or the wheels may need to be balanced