Foundations — Power — average and instantaneous, units

1.3.9 · D1 · Physics › Work, Energy & Power › Power — average and instantaneous, units

Yeh page kuch bhi assume nahi karta. Hum parent note ke har symbol se milenge, plain words mein samjhenge ki uska matlab kya hai, uski picture banaenge, aur explain karenge ki kyun yeh topic uske bina chal hi nahi sakta. Upar se neeche padho — har cheez upar wali cheez par build hoti hai.

1. Time, aur isko chop karne ke do tarike

Picture: ek timeline ko ruler ki tarah socho. Ruler par ek dot hai $t$. Do dots ke beech ka shaded band hai $\Delta t$. Us band ko squeeze karo jab tak woh ek hairline na ban jaye — woh hairline hai $dt$.

2. Work $W$ aur energy $E$ — joh cheez transfer ho rahi hai

Neeche wali picture: ek force arrow ek box ko distance tak drag karta hai, aur right side par energy ka shaded "tank" exactly $W$ se bhar jaata hai.

Dono joules (J) mein measure hote hain. Work Work — definition and W = F·d cosθ mein build hoti hai; woh poora note iss symbol ka prerequisite hai.

3. Force $\vec{F}$, displacement $\vec{s}$, velocity $\vec{v}$ — aur chhote arrows kyun

Picture: arrow ki length = size (iska "magnitude", $F$ bina arrow ke likha jaata hai), iska pointing = direction.

4. Angle $\theta$ aur uska shadow-maker $\cos \theta$

Do arrows rarely same direction mein point karte hain. Unke beech ka angle hai $\theta$ (Greek "theta"). Hume ek number chahiye jo bataye ki kitna alignment hai, aur woh number hai $\cos \theta$ ("cosine of theta").

Picture: velocity arrow ka "shadow" force arrow ki line par daalo. Us shadow ki length, poore arrow ki fraction ke roop mein, hi $\cos \theta$ hai.

Har case is ek dial se cover hota hai:

5. Dot product $\vec{F}\cdot \vec{v}$ — sab kuch ek dot mein pack karna

Toh dot koi naya mystery nahi hai — yeh exactly wahi "length $\times$ length $\times$ cosine" hai jo tumne abhi build ki. Isko Dot product of vectors mein fully spell out kiya gaya hai.

6. Limit $\underset{\Delta t\to 0}{\lim }$ aur derivative $\frac{dW}{dt}$

7. Symbols ko wapas master formulas mein daalna

Ab har letter earn ho gaya hai, aur parent ke boxed formulas plain English mein padhe ja sakte hain:

Prerequisite map

Equipment checklist

Apne aap ko test karo — right side cover karo. Agar koi bhi answer shaky lage, toh main note se pehle woh section revisit karo.

Connections

• Power — average and instantaneous, units (Hinglish) — woh parent topic jise yeh foundations feed karte hain.
• Work — definition and W = F·d cosθ — jahan $W$ aur $\cos \theta$ janam lete hain.
• Velocity and instantaneous rate (Kinematics) — $\vec{v}$ ke liye average-vs-instantaneous split.
• Dot product of vectors — $\vec{F}\cdot \vec{v}$ ki poori kahani.
• Kinetic Energy and Work-Energy Theorem — work $W$ ka ek aur source.
• Energy conservation and efficiency — jahan power flows compare hoti hain.