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

1.1.17 · Physics › Measurement, Vectors & Kinematics

FREE FALL kya hai?

Mass kyun matter nahi karta: Newton kehte hain $F = ma$ . Gravity $F = m g$ se kheenchti hai. Toh $ma = m g ⟹ a = g .$ Mass cancels ho jaata hai. Bhaari objects zyada force feel karte hain, lekin unhe accelerate karne ke liye zyada force bhi chahiye — yeh dono exactly balance ho jaate hain.

Sign conventions kaise setup karein

Convention A — "Up is positive" (sabse common):

Acceleration $a = - g = - 9.8 m/s^{2}$ (gravity neeche point karti hai = negative).
Upward velocity $+$ hai, downward velocity $-$ hai.
Start se upar ki height $+$ hai.

Convention B — "Down is positive" (sirf girne wali cheezon ke liye handy):

Acceleration $a = + g = + 9.8 m/s^{2}$ .
Downward velocity $+$ hai.

Dono same physics dete hain; jo initial conditions ko simplest banaye woh chuno.

Equations of motion scratch se derive karna

Hum constant acceleration $a$ se shuru karte hain (yahan $a = \pm g$ ). Acceleration, velocity ke change ki rate hai: $a = \frac{d v}{d t} .$

Step 1 — velocity. Kyun? $d v = a d t$ ko $a$ constant rakhte hue integrate karo: $\int_{v_{0}}^{v} d v = \int_{0}^{t} a d t ⟹ v - v_{0} = a t ⟹ v = v_{0} + a t .$

Step 2 — position. Kyun? Velocity hai $\frac{d y}{d t} = v_{0} + a t$ . Integrate karo: $\int_{y_{0}}^{y} d y = \int_{0}^{t} (v_{0} + a t) d t ⟹ y - y_{0} = v_{0} t + \frac{1}{2} a t^{2} .$ $y = y_{0} + v_{0} t + \frac{1}{2} a t^{2} .$

Step 3 — time-free relation. Kyun? $t$ eliminate karo taaki $v$ aur displacement ko relate kar sako. Step 1 se, $t = (v - v_{0}) / a$ . Step 2 mein substitute karo aur simplify karo: $v^{2} = v_{0}^{2} + 2 a Δ y .$

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

Key consequences (woh 80/20 jo zyaatar problems solve karta hai)

Top tak time: $v = 0$ set karo $v = v_{0} - g t \Rightarrow t_{up} = v_{0} / g$ mein.
Max height: $H = v_{0}^{2} / (2 g)$ from $0 = v_{0}^{2} - 2 g H$ .
Up–down symmetry: time up = time down; ball launch height pe waapas aati hai $v_{0}$ speed ke saath (lekin neeche ki taraf, yaani $- v_{0}$ ).

Worked examples

Common mistakes (steel-manned)

Recall Feynman: ek 12-saal ke bachhe ko samjhao

Imagine karo tum ek ball seedha upar phenkate ho. Gravity ek aisi invisible hand hai jo hamesha neeche kheenchti hai, poore waqt same amount mein. Upar jaate waqt yeh pull ball ko slow karti hai; ek chhote se instant ke liye top pe woh move nahi kar rahi; phir wohi pull use neeche aate waqt speed up karti hai. Har object — ek bowling ball ya ek marble — har second same amount se speed up hota hai (lagbhag har second 10 m/s zyada), jab tak koi hawa peeche nahi dha rahi. Jo "+ aur –" hum use karte hain woh sirf "up" aur "down" likhne ka tarika hai taaki math confuse na ho.

Active recall

Free fall kya hai?

Sirf gravity ke under motion (koi air resistance/doosri forces nahi); acceleration

= g \approx 9.8 m/s^{2}

downward.

Saare masses ek hi acceleration se kyun girte hain?

Kyunki

ma = m g

⟹

a = g

; mass cancel ho jaata hai.

"Up positive" ke saath, freely falling object ki acceleration kya hai?

a = - g = - 9.8 m/s^{2}

Vertical throw ke highest point pe velocity aur acceleration kya hain?

v = 0

, lekin

a = - g

(gravity phir bhi act kar rahi hai).

v_{0}

se upar launch karne pe top tak pahunchne ka time?

t_{up} = v_{0} / g

v_{0}

launch speed se seedha upar ke liye maximum height?

H = v_{0}^{2} / (2 g)

Teen constant-acceleration equations (up positive)?

v = v_{0} - g t

;

y = y_{0} + v_{0} t - \frac{1}{2} g t^{2}

;

v^{2} = v_{0}^{2} - 2 g Δ y

Upar pheki gayi ball launch height pe waapas kaunsi speed se aati hai?

Same magnitude

v_{0}

lekin neeche ki taraf directed (

- v_{0}

Path ke top pe acceleration zero kyun nahi hoti?

Velocity momentarily zero hoti hai lekin gravity band nahi hoti;

a = - g

continuously rehta hai.

Connections

Equations of Motion (constant acceleration)
Vectors and sign conventions
Projectile Motion — free fall vertical component hai
Newton's Second Law — $a = g$ ka source
Air Resistance and Terminal Velocity — jo free fall ko todta hai