1Force, vigor, or energy — the drive or vitality behind a person or an action.
新人選手は勢いのあるプレーでファンを沸かせた。
The rookie player thrilled fans with vigorous, energetic plays.
子供たちは勢いよく坂道を駆け下りた。
The children ran down the slope with great energy.
彼のスピーチには勢いがあって聴衆を引きつけた。
His speech had such vigor that it captivated the audience.
2Influence, authority, or power — the strength or standing that a person, group, or force commands.
新興企業が業界で急速に勢いを伸ばしている。
The up-and-coming company is rapidly gaining influence in the industry.
その武将は一時、天下を治めるほどの勢いを誇った。
That warlord once boasted enough power to rule the whole land.
反対派の勢いに押され、法案は取り下げられた。
Pushed back by the strength of the opposition, the bill was withdrawn.
3The momentum or impetus of the moment carrying an action forward; often used as '勢いで～する' (to do something on the spur of the moment).
飲み会の勢いで、思わず旅行の約束をしてしまった。
Carried away by the mood at the drinking party, I ended up promising to go on a trip.
一度火がついた議論は勢いを増していった。
Once the debate caught fire, it gained more and more momentum.
4As a natural or inevitable consequence of what precedes; a somewhat literary connective adverb meaning 'naturally' or 'necessarily'.
人口が減れば、勢い、地域の経済も縮小する。
If the population declines, the local economy will inevitably shrink as well.
準備に時間をかけなかったので、勢い、結果も中途半端になった。
Since little time was spent preparing, the result was naturally half-baked as well.