Something is moving. I have an automatic 3.0 4x4. Its a 2000. At times when I accelerate from a stop I feel something up front move. I can't make it happen. It feels like maybe the engine moves. Just slightly. Also today I felt something move at about 60 mph. It felt like a downshift. It wasn't dramatic. But it felt like the transmission or the engine moved. Sort of how a stick feels. Any ideas on this? Seems like sometimes when I slow down to a stop it happens also. Usually in slow traffic.
Feels a bit like something is rocking a little.

 

Test Motor mounts

Hood open
Start engine
Shift into D(or 1st)
Foot on the brake, give it some gas(or engage trans with clutch)
Watch if engine Lifts up, then release gas quickly and listen for clunk
Repeat but use Reverse

Engine will lift slightly but not alot, if too much, or you hear a clunk, then mount on that side is broken