There could be many causes ranging from a bad spark plug that fails when combustion chamber pressures rise to frozen half shafts. If the vibration is only felt when you accelerate from the same speed or when passing through the same speed you might suspect tire imbalance.
Of course if it's a Generation I Solara convertible then the answer is "they all do it" to some extent. The early ragtop is known for its shimmies and shakes so the issue could even be a road surface.
Hopefully someone who owns a Gen I Solara will come along with an edit saying "mine did that and it was ......"
Cheers
Normally a bent wheel or tire out of balance.
A worn out Universal joint in the rear driveshaft.
Only when accelerating, I would suspect a broken motor mount or bad CV joint.
Could be in need of a tune up.
You need to check rotors and brake pads one or both are failing.
Engine Misfire? check engine light on? If so have vehicle scanned to determine the problem
Either your front end or your tires needs to be aligned.
191 K maybe it just wants to retire and hit the boneyard in the sky.
The transmission is not shifting in and out of gear or your front joint is going bad
This is Alzheimer's Disease.
oil chane
I was told by a buddy of mine who's a GM Master Tech that it's the Universal Joint in the axle. He said I'm better off just replacing the axle with a reman for a few dollars more.