Bash launch certain commands like being a root user without being root user

I've the following problem.

When I launch df command being a usual user of machine it outputs what I need:

But when I try to launch it from another user (www-data in this case) I have problems with permissions:

I understand that this is because user www-data doesn't have enough privileges. But I don't want to up his privileges.

It would be perfect to allow this user to launch only some programs as root without entering the root password without increasing its privileges. It's ok if I'll be asked to enter root's password one time and will be able to run command with full privileges without entering root password anymore.

Note:

I have root access to machine.

Can it be reached somehow?