(a) The owner of any vehicle first acquired or first used in the city or town after July 1 of the taxable year shall be required to pay only one-half (½) of the annual rate of the city or town vehicle tax for the remainder of the calendar year. The tax may be paid, without penalty, during the thirty-day period following the date of first acquisition or first use.
(b) No vehicle tax shall be required of the owner if the vehicle tax for the particular year has been paid by a former owner, whether or not in the same city or town.