Why would an orange roll of your cafeteria tray if you stopped suddenly

Because the frictional force between the orange skin peel is great enough when you are walking for it to be carried on the tray, along with the gravitational force downwards onto the tray. When you stop, the force that you exerted moving forward it the same as on the tray and on the orange. So when you stop, the force is still on the orange as the same velocity as your we're traveling, while the tray and you stop.