Free fall — g = 9.8 m - s², sign conventions: Foundations

1.1.17 · D1 · Physics › Measurement, Vectors & Kinematics › Free fall — g = 9.8 m - s², sign conventions

Is page pe assume kiya gaya hai ki aapne kuch bhi nahi dekha. Hum har letter, symbol aur picture ko build karte hain jo parent note Free-fall page use karta hai, us order mein jo har ek ko pehle wale par lean karne deta hai.

0. "Position axis" hota kya hai

Ball kahan hai yeh kehne se pehle, hume ek ruler chahiye jo duniya mein pini ho. Ek point choose karo jise zero bologe, uske through ek seedhi line kheecho, aur ek direction mein equal steps ( $1, 2, 3, \dots$ metres) mark karo aur doosri direction mein ( $- 1, - 2, - 3, \dots$ ).

Figure — Free fall — g = 9.8 m - s², sign conventions

Aapne jo direction positive choose ki hai woh aapka sign convention hai. Neeche sab kuch usi par depend karta hai.

1. Direction as a sign: $+$ aur $-$

Hamare ruler par, arrow direction (maan lo, upar) $+$ hai aur opposite (neeche) $-$ hai. Koi quantity jisme size bhi ho aur line-along-direction bhi ho, woh vector ka sabse simple type hai, aur ek seedhi line par ek vector sirf sign ke saath ek number hota hai.

2. Time: symbol $t$

3. Velocity: symbol $v$ aur uske peeche ka ratio

Ball ko thodi si distance $Δ y$ move karte dekho ( $Δ$ symbol, Greek "D", matlab "change in" — end value minus start value) thode se time $Δ t$ mein.

Jab hum $Δ t$ ko ek instant ki taraf shrink karne dete hain, yeh ratio instantaneous velocity ban jaata hai, lika jaata hai $\frac{d y}{d t}$ (dekho §5).

4. Acceleration: symbol $a$ aur kyun $g$ special hai

Velocity khud bhi change ho sakti hai. Acceleration measure karta hai ki velocity kitni tez change hoti hai.

5. Derivative $\frac{d v}{d t}$ — kyun calculus aata hai

Parent likhta hai $a = \frac{d v}{d t}$ . Yeh §3–4 ka ratio hai jo time ke ek instant ki limit tak le jaaya gaya hai, na ki time ke ek chunk ki.

6. Force–mass link: $F = ma$ aur mass cancel kyun hota hai

Gravity ek force $F = m g$ se kheenchti hai. Use $F = ma$ mein daalo: $ma = m g ⟹ a = g .$ $m$ cancel ho jaata hai — dono sides par aata hai, divide ho jaata hai. Isi wajah se vacuum mein ek hammer aur ek feather same tarah girte hain: zyada mass zyada pull feel karta hai, lekin resist bhi zyada karta hai, aur dono exactly balance kar lete hain.

y

kya represent karta hai, aur

x

kyun nahi?

Ruler par position batane wala number;

y

isliye use karte hain kyunki free fall vertical hai.

Kisi quantity ke aage

Δ

(Greek D) ka matlab kya hai?

"Change in" — final value minus initial value.

"Up is positive" axis par, negative velocity ka physically kya matlab hai?

Object neeche move kar raha hai (sign = direction, slow nahi ho raha).

g

aur

a

mein kya fark hai?

g

ek fixed positive size hai (

9.8

);

a

woh acceleration hai jiska sign (

+ g

- g

) aapke convention par depend karta hai.

Velocity ratio

Δ y /Δ t

ke roop mein kyun define ki jaati hai?

Yeh "per unit time kitni position?" ka jawab deta hai — distance aur duration dono ek saath capture karta hai.

Derivative

d v / d t

kya deta hai jo

Δ v /Δ t

nahi deta?

Ek exact moment par instantaneous rate of change, na ki kisi chunk ka average.

F = ma

mein jab gravity

F = m g

hai, mass cancel kyun hota hai?

Dono sides par

m

hai; use divide karne par

a = g

milta hai, isliye acceleration mass se independent hai.

v_{0}

y_{0}

mein subscript

0

ka kya matlab hai?

Start par, jab

t = 0

ho, us waqt ki value (initial velocity / initial position).

Connections

Free fall — g = 9.8 m - s², sign conventions — woh topic jiske liye yeh foundations build ho rahe hain
Vectors and sign conventions — jahan se signs-as-directions aata hai
Equations of Motion (constant acceleration) — woh integration jo kit produce karta hai
Newton's Second Law — $a = g$ ka source
Projectile Motion — vertical part ke liye yahan ke har symbol ko reuse karta hai

Foundations — Free fall — g = 9.8 m - s², sign conventions