I recently did ubuntu update and then after reboot i got following screen related to kernel panic. The problem for me was that my /boot ran out of space.
Restart your machine and go to grub loader
Select "Advanced options for Ubuntu"
Then you will be listed with list of kernels, select one of them and press enter [at least one of them should allow to you boot and login into your ubuntu machine]
Then go to terminal and run:
aptitude search ~ilinux-image
this should list all the kernel images u have in /boot
to get ur current running kernel
sudo apt-get <image name>
for example: sudo apt-get autoremove linux-image-4.4.0-45-generic
to remove the image that you dont need