So im not sure how you want the Cart to move, do you want it so it moves when it's pushed to a certain location, or do you want it to be pushed using logic_relays? I have both solutions here
1. AFTER BEING PUSHED
Place a path_track where you want the cart to start moving on it's own, make sure the path_track has these Outputs:
OnPass -> cart_tracktrain -> SetSpeedDir -> 1
(The Pushzone Trigger should also be disabled while the Cart moves, if someone pushes it, it stops moving automatically)
2. LOGIC_RELAY
Place a logic_relay and add these Outputs:
OnTrigger -> cart_tracktrain -> SetSpeedDir -> 1
OnTrigger -> cap_area (pushzone) -> Disable