Sounds like you're looking for something that configures the DPI/sensitivity profiles on the mouse. There's no universal app to set this up. You have to find the manufacturer of the mouse and see if they have an app that supports yours.no, I meant, the mouse moved slower if you moved slowly but I could set it up so the faster you move it, the further the cursor moved. It had sliders for like about 5 different speeds. I had it set up so it barely moved if you move the mouse slow, but if you moved it fast, it the cursor would fly from one side of the screen to the other in one quick motion. (the same distance moves different distance depending on speed of the mouse movement.)
It sounds like "acceleration" is the keyword that you are looking for. Or "acceleration curve". A quick Google search for "acceleration mouse movement software" brings up several such applications.