Thanks, Alvaro, for your answer, and sorry for delay. Please find below the ouputs from the commands you asked me to run and other informations:
Welcome to Ubuntu 14.04.2 LTS (GNU/Linux 3.13.0-55-generic x86_64)
55 packages can be updated.
30 updates are security updates.
vagrant@vagrant-ubuntu-trusty-64:~$ vagrant ssh
The program 'vagrant' is currently not installed. To run 'vagrant' please ask your administrator to install the package 'vagrant'
vagrant@vagrant-ubuntu-trusty-64:~$ sudo df -h
Filesystem Size Used Avail Use% Mounted on
/dev/sda1 40G 2.0G 36G 6% /
none 4.0K 0 4.0K 0% /sys/fs/cgroup
udev 240M 12K 240M 1% /dev
tmpfs 49M 344K 49M 1% /run
none 5.0M 0 5.0M 0% /run/lock
none 245M 0 245M 0% /run/shm
none 100M 0 100M 0% /run/user
vagrant@vagrant-ubuntu-trusty-64:~$ sudo mount
/dev/sda1 on / type ext4 (rw)
proc on /proc type proc (rw,noexec,nosuid,nodev)
sysfs on /sys type sysfs (rw,noexec,nosuid,nodev)
none on /sys/fs/cgroup type tmpfs (rw)
none on /sys/fs/fuse/connections type fusectl (rw)
none on /sys/kernel/debug type debugfs (rw)
none on /sys/kernel/security type securityfs (rw)
udev on /dev type devtmpfs (rw,mode=0755)
devpts on /dev/pts type devpts (rw,noexec,nosuid,gid=5,mode=0620)
tmpfs on /run type tmpfs (rw,noexec,nosuid,size=10%,mode=0755)
none on /run/lock type tmpfs (rw,noexec,nosuid,nodev,size=5242880)
none on /run/shm type tmpfs (rw,nosuid,nodev)
none on /run/user type tmpfs (rw,noexec,nosuid,nodev,size=104857600,mode=0755)
none on /sys/fs/pstore type pstore (rw)
rpc_pipefs on /run/rpc_pipefs type rpc_pipefs (rw)
systemd on /sys/fs/cgroup/systemd type cgroup (rw,noexec,nosuid,nodev,none,name=systemd)