I have a carrier furnace and when I switch to heat on the tstat the inducer fan comes on then the burners ignite then the blower motor comes on, after about 45 seconds or so the blower motor and burners cut off but the inducer fan keeps running and this process starts again in 10 to 15 minutes with the inducer fan never cutting off what could be the problem

Weak main limit, poor airflow, dirty filter or evaporator coil or insufficient supply and/or return air.