Drive shaft play/possible worn/bad ujoints /driveshaft
Your gear linkage is offset!! Or you are on a steep down hill
Bad shocks
It could be the transmission, it could be some parts under the vehicle that rub only when travelling forward.
check shocks
Engine idle too high.
This could be the breaks needing replaced, could be a wheel bearing that needs replaced.
A reversible process is one which can be reversed and causes no changes in the system or surroundings. For a process in equilibrium, the rate of the forward process equals the rate of the reverse process (which can be, but is not necessarily equal to zero).
Check to see if your trunk is open or if the clasp that holds it closed is loose.
Most likely your upper shock mounts. Get them checked over.
If your truck is 2wd than check the bearing, hub assembly. This is considering that you have the balance and alignment checked at a shop already
check rack and pinion. sounds like it needs to be replaced.
have you car checked out at a transmission shop.