Hard acceleration 1st and 2nd and clunk in rear

No, it's not common. Under hard acceleration or braking, the axle housing attempts to twist itself under the car: on acceleration, the pinion attempts to move "upwards" as the axle housing reacts to torque input from the driveshaft. Under braking (while moving forward), the pinion moves "down" as the brake calipers apply torque to the housing. Such movements are controlled by the upper and lower control arms. First thing I'd do is get the car on a hoist or jackstands and check for damage or corrosion in the areas where the upper control arms mount to the body (sheetmetal brackets spotwelded to the floor.) If they look solid, you may have a bushing that's pulled-through or has gone oval.

There is also a "pinion snubber" that limits the wind-up of the rear axle. The axle housing may be hitting the snubber during a hard launch (axle wind-up plus rear-squat) causing a noise, especially if your car is lowered. Check for witness marks on the housing or snubber.

You might want to verify that the U-joint at the rear of the driveshaft is not loose or worn.

narib2008 said:

I will look again.The car only has 66k miles and there is really no visible bushing damage.I did have uj problems on my previous mustang and i replaced them.However i thought the u joints just kind of click/thump when they are worn and only when you are on or off acceleration?

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The forces on the rear axle and driveshaft during acceleration are prodigious. In 1st gear, at your engine's torque peak (~300 ft-lbs) you're feeding 1100 ft-lbs of torque to the pinion and driveshaft (300 ft-lbs x the 1st gear ratio of 3.37.)

I was spitballing some ideas and tossed U-joints in there at the end as a nod to the fact that there are non-trivial forces on all mechanical components back there, from the driveshaft to the control arm bushings, and that you should at least verify they're okay.