On my 1989 Toyota Camry while driving I will get to about 40 miles per hour and the car will not accelerate any more unless I ease up on the gas pedal and lightly accelerate . What is going on?

Check fuel pressure gas filter and check air filters

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One tank of gas is not enough to compare mileage. Or are you saying the computer's readout of mpg estimate is showing less? Try a tank or two of premium and see if that helps. Keep track of gas mileage. Driving techniques have a lot to do with gas mileage, as does long trips vs. short trips, highway cruising vs. city driving. For best mileage, do regular maintenance and keep the car in top running condition-good spark plugs and clean filters and clean oil ! Attend to minor problems before they escalate.
If you want to check actual miles per gallon, start with a full tank. Write the odometer reading down, and go. Everytime you put gas in, write down the amount. When you are close to 1,000 miles from the time you started, go fill the tank and include that amount of gas to your previous list. Now add up all the gas used and divide it into the miles to get miles per gallon. (976 miles/31.8 gallons = 30.69 mpg ) . Only one tank will skew your numbers, might be off cause the tank was filled more to the top than the previous fill-up. About a thousand miles of driving will give you a very accurate figure of miles per gallon for your car.

Have you had this problem long? is there a check engine light on? have you done any new repairs and then the problem come to be?

It sounds like one or both of the drive axle inner joints are worn out. This condition will give a very pronounced vibration on acceleration only and will be worse with increased speed.

Accelerate more slowly, and do not drive as fast. 21 is ok in the city, with automatic and AC. You can also use higher tire pressure, advance the ignition timing, turn off the AC, close the windows, etc.

If the engine revs up while in drive and running at 40mph, your transmission is probably slipping. Try checking your transmission fluid level. If it is OK, I would get it by a garage to have them look at it to cofirm.

no not muffler problem could be bad gas or TPS sensor how many miles you have on it?

the other guys is totally correct, at 349K miles, im surprised the car is even running any more.

my 2 cents -

1. You didn't specify your exact model, on this site you'll fond your answer - http://www.fueleconomy.gov/feg/bymodel/1989_Toyota_Camry.shtml

2. There are a few ways to do this, here's one -
- Fill your gas tank to the very top.
- Write down your odometer or reset you trip meter.
- Drive your car till it's time to fill it up again.
- When it's time to fill you tank, fill it to the very top (preferd in the same station, in the same pump).
- divide the number of miles (or kilometers) you drive, by the amount of gas you filled, This is of course only true for this gas tank, fuel consumption is effected by many things, load, driver, type of miles you do (city or hoghway), etc..

3. Service your car regularly, make sure tire pressure is correct, don't drive like you are racing.

Good luck,
Eitan.