颱風天，風一直吹。可是為什麼強陣風一來，招牌、路樹就倒一片？
根據中央氣象署觀測，薔琵颱風期間，全台有 87 個鄉鎮吹到 10 級強陣風（約每秒 25 公尺）。三貂角、桃源谷、大屯山甚至出現 17 級（每秒超過 56 公尺）。到 10 月 24 日下午，全台有 1,014 件招牌、廣告物災情。
風速只快一倍，力量真的只多一倍嗎？
※ 風速為氣象署觀測，計算為簡化示例｜插圖為 AI 生成
先猜猜看
風速從每秒 25 公尺變成每秒 50 公尺，風的動能變幾倍？
A. 2 倍 B. 4 倍 C. 差不多，空氣那麼輕
比特說：「快一倍，當然就是 2 倍啦！」
答案是 B，4 倍。
原來如此
① 動起來的東西都有能量
慢慢走撞到你，不太痛。跑著撞到你，很痛。差別就是動能（kinetic energy）。
動能等於二分之一，乘上質量，再乘上速率的平方：
K 是動能（單位焦耳 J），m 是質量（kg），v 是速率（m/s）。
空氣不是「沒重量」。1 立方公尺的空氣，質量約 1.2 公斤，差不多是一大瓶 1.2 公升的水。
② 第一步：已知
- 質量：m = 1.2 kg（1 立方公尺的空氣）
- 10 級強陣風：v₁ ≈ 25 m/s
- 速率快一倍：v₂ = 50 m/s
③ 第二步：代入
1.2 的一半是 0.6。
④ 第三步：答案與意義
速率變 2 倍，平方之後變 4 倍。速率變 3 倍，動能變 9 倍；速率變 4 倍，動能變 16 倍。
17 級陣風約每秒 60 公尺，動能約 2160 J，大約是 10 級的 5.8 倍。
下次你看到颱風新聞說「陣風又多兩級」，就會發現：動能多的不只一點點。颱風天請遠離招牌和路樹！
這在課綱的哪裡？
動能是能量的一種形式，屬於高中部定必修物理「能量」主題，是學測範圍。學測常考「速率變幾倍，動能變幾倍」的比例題，關鍵就是速率要平方。
想多練幾題？到 每天物理複習 做能量單元的練習。
常見迷思
風速快一倍，動能也只多一倍？
不對。動能和速率的「平方」成正比。快一倍，動能變 4 倍。
空氣很輕，所以風沒什麼能量？
空氣有質量，1 立方公尺約 1.2 公斤。颱風吹來的是一大片空氣，而且速率很大，所以能量很可觀。
算動能時，可以忘了二分之一？
不行。少了二分之一，答案會大一倍。
小測驗
1 立方公尺的空氣，質量約 1.2 公斤，風速每秒 30 公尺。它的動能約多少？
A. 18 J
B. 540 J
C. 1080 J
看答案
答案是 B，540 J。
① 已知：m = 1.2 kg，v = 30 m/s。動能公式：
$$K=\frac{1}{2}mv^2$$② 代入。1.2 的一半是 0.6。小心：30 的平方是 30 × 30 = 900，不是 30 × 2 = 60。
$$K=\frac{1}{2}\times1.2\times30^2=0.6\times900$$③ 答案與意義：
$$K=540\ \text{J}$$白話：540 J 大約能把一個 55 公斤的人抬高 1 公尺（55 × 9.8 ≈ 540）。
陷阱：選 A（18 J）是忘了平方；選 C（1080 J）是忘了乘二分之一。
資料來源
In English
On a typhoon day, the wind blows all day. So why do signs and trees fall when strong gusts come?
According to the Central Weather Administration (CWA), during Typhoon Champi, 87 townships had level 10 gusts (about 25 m/s). Sandiao Cape, Taoyuan Valley and Mount Datun even had level 17 gusts (over 56 m/s). By the afternoon of October 24, there were 1,014 reports of damaged signs and billboards.
The wind was only about twice as fast. Was it only twice as strong?
Guess first
The wind speed goes from 25 m/s to 50 m/s. How many times bigger is the wind's kinetic energy? A is 2 times. B is 4 times. C is about the same, because air is so light. Bit says, "Twice as fast, so of course 2 times!" The answer is B, 4 times.
Moving things carry energy
A friend walking into you does not hurt much. A friend running into you hurts a lot. The difference is kinetic energy. Kinetic energy is one half times mass times speed squared.
K is kinetic energy in joules (J), m is mass in kg, and v is speed in m/s. Air is not weightless. One cubic meter of air has a mass of about 1.2 kg, like a big 1.2-liter bottle of water.
Step 1: What we know
The mass is m = 1.2 kg (1 m³ of air). A level 10 gust is about 25 m/s. Twice as fast is 50 m/s.
Step 2: Plug in
Half of 1.2 is 0.6.
Step 3: The answer and what it means
Twice the speed gives 4 times the kinetic energy, because the speed is squared. Three times the speed gives 9 times, and four times the speed gives 16 times. A level 17 gust of about 60 m/s carries about 2160 J, about 5.8 times a level 10 gust.
Next time the news says "gusts are two levels stronger," you will know the energy is much bigger, not just a little. Stay away from signs and trees in a typhoon!
Where is this in the curriculum?
Kinetic energy is part of the "energy" topic in the required senior high physics course, so it is in the GSAT scope. A common GSAT question asks how many times bigger the kinetic energy gets when the speed is 2 or 3 times bigger. The key is to square the speed. For more practice, try Daily Physics Review.
Common mistakes
Twice the speed means twice the kinetic energy? No. Kinetic energy depends on the speed squared, so it becomes 4 times.
Air is light, so wind has little energy? Air has mass, about 1.2 kg per cubic meter. A typhoon moves a huge amount of air at high speed.
Can you skip the one half? No. Without it, your answer is twice too big.
Quiz
One cubic meter of air has a mass of about 1.2 kg. The wind speed is 30 m/s. About how much kinetic energy does it have? A is 18 J. B is 540 J. C is 1080 J. The answer is B, 540 J.
Step 1. We know m = 1.2 kg and v = 30 m/s. Use K = ½mv².
Step 2. Plug in. Half of 1.2 is 0.6. Be careful: 30 squared is 30 × 30 = 900, not 30 × 2 = 60.
Step 3. K = 540 J. That is about the energy to lift a 55 kg person by 1 meter. If you chose A, you forgot to square the speed. If you chose C, you forgot the one half.