Each and every city within this state that now has or may hereafter have a population of over four thousand and less than thirty thousand inhabitants (that is now or may hereafter be incorporated and operating under the general statutes or special charter) shall have and is hereby given power and authority, by ordinance, to levy and collect a license tax upon each and every vehicle (whether used for hire or for private use or pleasure), propelled by horse power or by other domestic animals or propelled by steam or electricity, gasoline, denatured alcohol or other like motive powers, that are owned and operated within the corporate limits of such city, and the moneys derived from such license tax shall be placed in a special fund of such city and shall be expended in the maintenance, cleaning and repairs of the streets or other highways within such city, and for no other use or purpose whatever, and to provide for fines and penalties for the violation of such ordinance; and said license tax may be graduated according to the use and character of the vehicle; provided, however, that all vehicles of the same class shall be taxed alike.