I maybe am posting this in the wrong section, I am not sure.

Is there a way to protect an app to where it will require a password? This machine has one user that is used by more than one person. I have it as one user just to save time because people switch off using it all of the time, but I have one application that I would like only certain people to have access to. How would I do this?

Since you said "certain people" I'm assuming that means more than one, so here's how I'd do it. If somebody has a better solution feel free to post it, I don't claim to be a Linux expert, I've been using it off and on for years and I learn something every day.

1) Locate the binary executable, probably in /usr/bin or /bin or some similar location. It's the binary file that all the shortcuts point to that actually launches the application.
2) Create a group just for launching this application. Add only users you want to launch the application to the group.
3) Modify ownership of the binary file for the app so that your new group is now the owning group, and that you are the owner, and that "others" have no access to it at all.

If you're going to give up all effective control of your machine, you have to expect bad things to happen. It doesn't take all that long to log out and have someone else log in. Add some more users.

This is true, however when it is a lot of people who need to use the machine, that is a lot of logging in and out.

I considered just adding a second user, and all of the people who require access could log on as that user, but then it is still logging in and out a lot. I think I'll give the group idea a shot and see how that works first.

Quads:

Advices above are based on sound principles: it is really important to use several usernames for security reasons.

The most common solution to your request is given by dudeman41465 above. Its philosophy is this:

"Create a group of users that are permitted to the executable and have the ownership belong to them alone."

sudo chmod 750 /bin/my_executable.sh

Goodluck.