I am at an impasse. I can touch an object with my finger and it will follow the movement. What I then want is for the object to continue in a decaying arch once I have picked up my finger. I have all of my touch controls in the FinalUpdate function. Any help would be appreciated.
If your object is a rigidbody you could add a force to it that is proportional to your finger's movement speed before you release the object.
If it's not a rigidbody you could implement a kind of smoothing for the acceleration of the object. On release start a coroutine that interpolates you movement speed between last known speed and 0 over a given time.
This tutorial has an interesting inertia code after dragging and rotating an object, you might find it useful.
source code is here:
http://www.revelopment.co.uk/tutorials/unitytutorials/73-howtorotateanobjectbytouch