Q:

where is current directory when Ubuntu 16.04 automatically starts an application at power up

When I set up my program with Ubuntu > System menu > Preferences > Personal > Startup Applications, and then cycle power on the Linux SBC, when my application starts, which directory does it start in?

A:

The first directory would be your default directory (~userid).  Unless you changed it from the default it would be /home/yourid.
Some applications might change the current work directory as part of its configuration.  So if you see an occasion to be in a different folder, it would be, because of the operation of the particular app.
You can actually write a simple script/application to test this.
The  script:
myscript.sh:
#!/bin/bash

date >> /tmp/test.out
echo "Current Workdirectory: $(pwd)" >> /tmp/test.out

Create a desktop launcher and place it in your ~/.config/autostart folder:
The desktop launcher:
myapp.desktop:
#!/usr/bin/env xdg-open                                                                                                  
[Desktop Entry]
Name=My Test App
GenericName=Test Application
Comment=A quick test script
Exec=/usr/local/bin/test.sh
Terminal=false
Type=Application
Icon=/usr/share/icons/local/apollo.png
Categories=test;script
StartupNotify=false

Save the test.sh file at /usr/local/bin.  Make sure it is executable with chmod +x test.sh.
It will automatically run.  You can then view the current directory by examining the redirected /tmp/test.out content.  It'll contain the date it was last run, plus your current work directory.
Tested Output:
$ cat /tmp/test.out 
Wed May 24 16:53:28 EDT 2017
Current Workdirectory: /home/apollo

