Triggered Rigit Body simulation with Logic

First, make sure you have set Render Engine as Blender Game!

1. Set object as Rigid Body as normally.
2. Open Logic Editor.
3. Add Sensor and set it as "Always".
4. Add Controller "And".
5. Add Actuator "Edit Object" and change it as "Dynamics" and Operation as "Suspend Dynamics"
6. Add another Sensor "Delay". Set Delay value as you wish (If value is 50, Rigid Body simulation starts when time hits 50).
7. Add Controller "And".
8. Add Actuator "Edit Object" and change it as "Dynamics" and Operation as "Restore Dynamics"
9. Finally, connect them together just like on image above.