IPA: /ɛkˈstɛmpəˌrɛli/
KK: /ɛkˈstɛmpəˌrɛri/
In a way that is done without preparation or planning, often speaking or performing spontaneously.
She delivered her speech extemporarily, impressing everyone with her ability to think on her feet.
Extemporarily → It is formed from "ex-" (meaning out of or from) and "temporarius" (from Latin, meaning temporary or of time). The word "extemporarily" means done or spoken without preparation, as if coming out of the moment or time.
Think of something happening 'out of' ('ex-') the 'moment' ('temporarius') — that's why extemporarily means something done spontaneously or without prior planning.