Kinetic energy — derivation — Hinglish notes

1.3.4 · Physics › Work, Energy & Power

Kinetic energy KYA hai?

WHY scalar? Kyunki yeh work ( $W = F \cdot d$ , ek dot product) se aur $v^{2}$ (jo direction ignore karta hai) se bana hai. Energy ki koi direction nahi hoti.

Hum ise KAISE derive karte hain (first principles se)

Hum work ki definition aur Newton ke second law se shuru karte hain. Koi memorised formula allowed nahi hai.

Formula Step-by-step derivation

Step 1 — Net force dwara kaam. Ek constant net force $F$ , motion ke saath $s$ displacement par act karta hai: $W = F s$ Yeh step kyun? Work = force × displacement, yahi mechanical energy transfer ki definition hai.

Step 2 — $F$ ko Newton ke 2nd law se replace karo. $F = ma$ : $W = m a s$ Yeh step kyun? Hum jawaab motion ( $v$ ) ke terms mein chahte hain, isliye force ko mass × acceleration se trade karte hain.

Step 3 — $a s$ express karne ke liye kinematics use karo. Rest ( $u = 0$ ) se speed $v$ tak motion ke liye: $v^{2} = u^{2} + 2 a s \Rightarrow v^{2} = 2 a s \Rightarrow a s = \frac{1}{2} v^{2}$ Yeh step kyun? Yeh kinematic relation $a$ aur $s$ ko final speed se link karta hai, woh variables hata deta hai jo humein nahi chahiye.

Step 4 — Substitute karo. $K = W = \frac{1}{2} m v^{2}$ Yeh step kyun? Jo kaam andar daala gaya woh motion ki stored energy ban jaata hai — woh stored amount hi kinetic energy hai.

General (calculus) derivation — tab bhi kaam karta hai jab force vary kare

Yahi Work–Energy Theorem hai: ==net work done = change in kinetic energy==, $W_{n e t} = K_{f} - K_{i} = \frac{1}{2} m v_{f}^{2} - \frac{1}{2} m v_{i}^{2} .$

Worked examples

Common mistakes (steel-manned)

Recall Feynman: 12-saal ke bacche ko samjhao

Socho tum ek toy car dhakka de rahe ho. Jitna zyada aur jitni der dhakka doge, utni tezi se jaayegi — tum usme "go-energy" bhar rahe ho. Agar result mein car do guna tez ho jaaye, toh woh sirf do guna zyada takkar nahi legi, woh chaar guna zyada takkar legi, kyunki energy speed ke square ke saath chalti hai. Woh stored "go-energy" hi kinetic energy hai: weight-ish number ka aadha, speed se speed se gunakarit.

Active-recall flashcards

Kinetic energy words mein kya hai?

Woh kaam jo ek body ko rest se uski current speed tak laane mein laga.

Kinetic energy ka formula?

K = \frac{1}{2} m v^{2}

Derivation mein kaun si kinematic equation use hoti hai?

v^{2} = u^{2} + 2 a s

, jo rest se

a s = \frac{1}{2} v^{2}

deta hai.

Work–energy theorem batao.

Net work = change in kinetic energy,

W_{n e t} = K_{f} - K_{i}

Agar speed teen guni ho jaaye, toh kinetic energy kitni baar multiply hogi?

9 (kyunki

K \propto v^{2}

Kinetic energy scalar kyun hai?

Yeh dot product (work) aur

v^{2}

se bana hai, dono directionless hain.

Kya kinetic energy negative ho sakti hai?

Nahi, kyunki

v^{2} \geq 0

; sirf iska change negative ho sakta hai.

Kinetic energy ki unit?

Joule (J) = kg·m²/s².

Calculus derivation mein

\int F d s

ko konsa substitution convert karta hai?

\frac{d s}{d t} = v

, jo

\int m v d v

deta hai.

Kinetic energy — derivation

Kinetic energy KYA hai?

Hum ise KAISE derive karte hain (first principles se)

General (calculus) derivation — tab bhi kaam karta hai jab force vary kare

Worked examples

Common mistakes (steel-manned)

Active-recall flashcards

Connections

Concept Map