Describing Motion Around Us (Hamare Aas-paas ki Motion ka Varnan): Class 9 Science Chapter 4 Hinglish mein

Exploration · Hinglish notes, simulations aur practice · Official NCERT chapter PDF ↗

Published 13 Oct 2026 · Updated 13 Oct 2026

95 min
24 practice questions
26 MCQs

Is chapter mein aap kya seekhenge

Kisi reference point se distance aur direction (+ ya −) lekar object ki position batana, aur tay karna ki woh rest mein hai ya motion mein
Distance travelled aur displacement mein fark karna, aur seedhi line ki trips ke liye dono calculate karna, un trips ke liye bhi jo wapas mudti hain
SI units aur signs ke saath average speed, average velocity aur average acceleration calculate karna, aur km/h ko m/s mein badalna
Data se position–time aur velocity–time graphs plot karna, aur slopes se velocity aur acceleration, aur areas se displacement padhna
Constant acceleration ke liye v = u + at, s = ut + ½at² aur v² = u² + 2as derive karna aur unhe use karna, jaise stopping distances nikaalne ke liye
Samjhana ki uniform circular motion accelerated kyun hoti hai, aur circular path par distance, displacement aur average speed nikaalna

NCERT Science Class 9, Chapter 4, pp. 48–71 par based original companion text. Yeh NCERT se juda nahi hai aur NCERT ne ise endorse nahi kiya hai.

Ek minute ke liye bus ki khidki se bahar dekho aur gino ki kya-kya chal raha hai. Shayad tumhe lanes ke beech ghoomta-ghaamta scooter dikhe, kisi dukaan mein ghoomta ceiling fan, jhoole par ek bachcha, paani ki tanki ke upar chakkar kaatte kauve aur chhaton ke upar se khisakte monsoon ke baadal. Motion har jagah hai, aur zyadatar motion complicated hoti hai.

Koi is sab ka varnan kaise kar sakta hai? Trick yeh hai ki simple, idealised motions se shuru karo aur unhi se aage badho. Pichhli classes mein tum aisi teen motions se mil chuke ho. Woh hain seedhi line mein motion (linear motion), circle ke around motion (circular motion) aur ek fixed point ke aage-peeche motion (oscillatory motion). Yeh chapter pehli do ko kaafi aage le jaata hai. Tum naye quantities se miloge, displacement, velocity aur acceleration, aur seekhoge ki motion ko sirf words se hi nahi, numbers, graphs aur equations se bhi kaise describe karte hain.

4.1 Seedhi Line mein Motion

Sabse simple motion seedhi line mein hoti hai. Elevated track ke seedhe hisse par chalti metro train seedhi line mein chalti hai. Waise hi ungliyon se fisal kar farsh par girti chaabi aur apni lanes mein race karte swimmers bhi. Aisa object kaise chalta hai, yeh batane se pehle hume yeh batane ka tareeka chahiye ki har pal woh kahan hai.

4.1.1 Position batana

Maan lo koi kehta hai ki fruit cart "chaalees metre door" hai. Kahan se chaalees metre, aur kis taraf? Position pakki karne ke liye hum pehle ek fixed point chunte hain jahan se naapte hain; use reference point ya origin kehte hain. Phir object ki position do cheezon se milti hai: woh reference point se kitni door hai, aur kis direction mein.

Definition

Reference point (origin)

Ek fixed point jahan se positions naapi jaati hain. Position is point se distance aur direction batati hai.

ExampleFig. 4.1 mein bus stop.

Seedhi sadak par sirf do directions hoti hain, isliye hum sadak ko ek number line ki tarah bana sakte hain jismein origin O zero par ho. Ek direction ko positive aur doosri ko negative kehte hain. Aadat se, O ke right wali position ko + sign milta hai aur left wali ko − sign. Fig. 4.1 mein bus stop origin hai: cart +40 m par hai aur dog −40 m par. Dono 40 m door hain, lekin signs dikhate hain ki woh opposite sides par hain.

2/3Same distance, opposite signs: cart +40 m par hai, dog −40 m par.

Fig. 4.1Position = reference point se distance + direction (sign).NCERT Fig. 4.3 · p. 50

Ek seedhi gali number line ki tarah bani hai jis par −60 se 60 metre tak nishan hain, aur zero par ek bus stop ka sign hai jis par reference point O likha hai. Right ki taraf ka arrow positive side aur left ki taraf ka arrow negative side dikhata hai. Step 1 mein sirf origin aur do directions hain. Step 2 mein +40 m par ek fruit cart aur −40 m par ek dog aata hai, dono O se same distance par lekin opposite sides par. Step 3 kuch seconds baad ka hai: cart ab bhi +40 m par hai aur us par at rest likha hai, jabki dog chal kar −20 m par pahunch gaya hai aur us par moving likha hai.

Ab hum theek-theek bata sakte hain ki motion kya hai. Jis object ki position, reference point se naapi gayi, time ke saath badalti rehti hai, woh motion mein hai. Jiski position fixed rehti hai, woh rest mein hai. Fig. 4.1 ke last step mein, kuch seconds baad, cart ab bhi +40 m par hai, isliye woh rest mein hai. Dog −40 m se −20 m tak gaya hai, isliye woh chal raha hai. Koi cheez rest mein hai ya nahi, yeh is par depend karta hai ki tum kaunsa reference point chunte ho. Train mein soya passenger train ke hisaab se rest mein hai, lekin platform ke hisaab se motion mein.

4.1.2 Distance travelled aur displacement

Ananya seedhi sadak par apne ghar O se apni friend ke ghar F tak cycle chalati hai, jo 600 m east mein hai. Phir use yaad aata hai ki ek notebook chahiye, aur woh ghar ki taraf 250 m wapas ek shop S tak jaati hai (Fig. 4.2). Usne kitna travel kiya, aur woh aakhir mein kahan pahunchi?

Uske pahiye jitne metre ghoome, sab jodo: 600 m + 250 m = 850 m. Yeh total distance travelled hai. Yeh poora path ginta hai, direction chahe jo ho. Ab sirf yeh compare karo ki woh kahan se chali aur kahan ruki. Shop uske ghar se 350 m east mein hai. Position ka yeh net change uska displacement (विस्थापन) hai: +350 m, east ko positive lekar.

3/3S par: distance 850 m lekin displacement sirf +350 m.

Fig. 4.2Distance poora path jodta hai; displacement start ko finish se jodta hai.NCERT Fig. 4.4 · p. 50

0 se 600 metre ke scale wali ek seedhi sadak. Ghar O 0 par hai, shop S 350 m par aur friend ka ghar F 600 m par. Step 1: rider, ek dot, ghar par hai; distance 0 m aur displacement 0 m. Step 2: sadak ke saath ek arrow O se F tak ki ride dikhata hai; rider F par hai aur readouts distance 600 m aur displacement +600 m dikhate hain. Step 3: doosra arrow F se S tak wapas ki ride dikhata hai, aur O se S tak ek mota arrow hai jis par displacement likha hai; readouts distance 850 m aur displacement +350 m dikhate hain.

Definition

Displacement

Do instants ke beech kisi object ki position kitni aur kis direction mein khiski: jahan woh tha wahan se jahan woh pahuncha wahan tak ki seedhi line wali distance, aur pehle point se doosre point ki direction.

ExampleAnanya ka displacement east ki taraf 350 m hai.

Displacement poora batane ke liye uska magnitude (unit ke saath number, yahan 350 m) aur uski direction (east, ya + sign) dono chahiye. Distance travelled ke liye sirf magnitude kaafi hai. Dono metres (m) mein naape jaate hain, jo length ki SI unit hai. Jo trip wapas mudti hai, usmein distance badhti rehti hai jabki displacement ghat sakta hai. Agar Ananya cycle chala kar ghar tak chali jaati, to uska displacement zero ho jaata, halaanki usne 1200 m cover kiye hote.

Activity 4.1NCERT Activity 4.1 · p. 51

Yo-yo ka peechha karna

Tumhe chahiye

ek yo-yo, ya lambe dhaage se bandhi dhaage ki reel
ek metre scale
kaagaz ki ek patti, ek pen aur sticky tape

Pehle guess karo

Yo-yo neeche girta hai aur chadh kar wapas tumhare haath mein aata hai. Haath mein wapas aane ke baad, haath se uska displacement kya hai?

ZeroString ki poori lengthString ki length ka do guna

Darwaze ki frame ke paas kaagaz ki ek patti seedhi khadi chipkao. Apne haath ki height par 0 cm ka nishan lagao, phir uske neeche 25 cm, 50 cm aur 75 cm ke nishan lagao. Neeche ki direction ko positive lo.
Yo-yo ko 0 ke nishan par pakdo aur use khulne do. Dekho ki woh 25 cm ke nishan ko paar karta hai (is point ko P kaho), 75 cm par apne sabse neeche ke point B tak pahunchta hai, wapas chadhte hue 25 cm ke nishan ko paar karta hai (ise Q kaho) aur tumhare haath mein laut aata hai.
Har point ke liye nikaalo ki haath chhodne ke baad yo-yo ne total kitni distance travel ki, aur haath se uska displacement kitna hai. Table bharo.

Table 4.1

Point	Haath se total distance travelled	Haath se displacement
Haath (start)	0 cm	0 cm
P (neeche jaate hue)
B (sabse neeche ka point)
Q (upar jaate hue)
Haath (end)

Tumhari entries apne aap save hoti hain.

4/525 cm par upar jaate hue: distance 125 cm, displacement sirf 25 cm neeche.

Fig. 4.3Distance sirf badhti hai; displacement badhta hai, phir ghat kar wapas zero ho jaata hai.NCERT Fig. 4.5 · p. 51

Left mein ek vertical scale haath par 0 cm se neeche 75 cm tak jaata hai, aur neeche ki direction positive marked hai. Haath se string par ek yo-yo latka hai. Right mein distance travelled ka ek bar aur displacement ka ek bar 150 cm ki poori length ke against bharte hain. Step 1: yo-yo haath mein hai; dono bars khaali hain. Step 2: yo-yo 25 cm par neeche ja raha hai; dono bars 25 cm dikhate hain. Step 3: sabse neeche ke point, 75 cm, par dono bars 75 cm dikhate hain. Step 4: haath se 25 cm neeche upar jaate hue, distance bar 125 cm dikhata hai lekin displacement bar ghat kar 25 cm reh gaya hai. Step 5: wapas haath mein, distance bar 150 cm par poora bhara hai aur displacement bar 0 cm par khaali hai.

Tumhari table aisi honi chahiye. P par: 25 cm, aur 25 cm neeche. B par: 75 cm, aur 75 cm neeche. Q par: 125 cm, lekin sirf 25 cm neeche. Wapas haath mein: 150 cm, aur 0 cm. Yo-yo ek hi vertical line par upar-neeche chalta hai, isliye yeh straight-line motion hai, chahe woh direction palat leta hai. Displacement wapas zero tak gir sakta hai jabki distance badhti rehti hai. Displacement ka size kabhi distance travelled se zyada nahi hota; dono tabhi tak barabar rehte hain jab tak yo-yo wapas nahi mudta.

4.1.3 Average speed aur average velocity

Distance aur displacement batate hain ki object kitni door gaya, lekin yeh nahi ki kitni jaldi. Uske liye hum time se divide karte hain. Class 7 mein tum average speed se mil chuke ho: poori cover ki gayi distance ko use cover karne mein lage time se divide karke ise nikaalte hain.

average speed = \frac{d}{t}

(4.1)

jahan

$d$: travel ki gayi total distance
$t$: time interval

Distance ki koi direction nahi hoti, isliye average speed ki bhi nahi hoti: yeh bas unit ke saath ek number hai, aur kuch nahi.

Kuch motions steady hoti hain aur kuch nahi. Table 4.2 mein do walkers ko dekho. Walker 1 har 10 s mein theek 12 m cover karta hai, aur agar tum chhote hisson ka time naapo to bhi yahi steady pattern milega. Aisi motion, jismein har barabar time interval mein barabar distance cover hoti hai, uniform motion kehlati hai: speed kabhi nahi badalti. Walker 2 har interval mein pichhle se thoda zyada cover karti hai, isliye uski motion non-uniform hai. Doosri non-uniform motions dheemi hoti jaati hain, ya baari-baari se tez aur dheemi hoti hain.

Table 4.2Do walkers dwara har 10 s mein cover ki gayi distance

Time interval	Walker 1	Walker 2
0–10 s	12 m	6 m
10–20 s	12 m	10 m
20–30 s	12 m	14 m
30–40 s	12 m	18 m

Lekin poore 40 s mein dono walkers 48 m cover karte hain, isliye unki average speeds same hain, $1.2 m s^{- 1}$ . Average bahut saari detail chhupa sakta hai.

Definition

Uniform motion

Constant speed par seedhi line mein motion: same length ke time intervals mein hamesha same distance cover hoti hai, intervals chahe kitne bhi chhote hon.

ExampleTable 4.2 mein Walker 1.

Example 4.1NCERT Example 4.1 · p. 52

Ek messenger peechha karke pakad leta hai

Ek pilgrim ek town se nikalta hai aur roz 5 yojanas chalta hai. (Yojana distance ki ek purani Indian unit hai.) Chaar din baad ek messenger usi sadak par uske peeche nikalta hai, jo roz 9 yojanas chalta hai. (a) Kitne din baad messenger use pakad leta hai, aur town se kitni door? (b) Maan lo, iske bajaay messenger usi subah nikla hota jis subah pilgrim nikla, aur woh us se 70 yojanas aage wale town se uski taraf chalta. Tab woh kab milte?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Speed ki ek kamzori hai: yeh direction ko ignore karti hai. $30 k m h^{- 1}$ par chal rahe do autos ek doosre ki taraf bhi ja sakte hain ya ek doosre se door bhi, aur sirf unki speeds se tum yeh nahi bata sakte. Jab direction matter karti hai to hum average velocity (औसत वेग) use karte hain: displacement ko time interval se divide karo.

\begin{aligned} average velocity \\ = \frac{displacement}{time interval} \end{aligned}

(4.2a)

v_{av} = \frac{s}{t}

(4.2b)

jahan

$v_{av}$: average velocity
$s$: displacement (position mein change)
$t$: time interval

Definition

Average velocity

Kisi object ka displacement, us time interval se divide kiya jismein woh hua. Iska magnitude bhi hota hai aur direction bhi.

Seedhi line par displacement ka sign average velocity mein bhi aa jaata hai: + displacement se + velocity milti hai, − displacement se − velocity. Dono averages length ko time se divide karke milte hain, isliye dono metres per second mein naape jaate hain, jise $m s^{- 1}$ ya m/s likhte hain. Speedometers aur road signs kilometres per hour, $k m h^{- 1}$ , use karte hain.

Average velocity rate of change ka hamara pehla example hai: ek quantity mein doosri quantity ke har unit change par kitna change hota hai. Yahan yeh per second position ka change hai, isliye average velocity batati hai ki average mein position time ke saath kitni jaldi badalti hai.

Example 4.2NCERT Example 4.2 · p. 53

Ananya ki ride, time ke saath

Fig. 4.2 mein Ananya ko ghar se friend ke ghar tak 150 s lagte hain aur wapas shop tak aur 100 s. East ko positive lekar, poori ride ke liye uski average speed aur average velocity nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Ruko aur socho

3 mein se 1

Ek bus 2 h mein 120 km east jaati hai aur phir 3 h mein 120 km wapas west aati hai. Poori trip ke liye uski average speed kitni hai, km/h mein?

km/h

Answer dekho

Answer 48 km/h

Average speed = total distance ÷ total time = 240 km ÷ 5 h =

48 k m h^{- 1}

. Do speeds (60 aur 40) ka average lekar 50 nikaalna ek aam galti hai: bus dheemi speed par zyada time bitati hai. Uski average velocity zero hai, kyunki woh wahin khatam hoti hai jahan se shuru hui thi.

4.1.4 Average acceleration

Aankhen band karke metro mein baitho, phir bhi tum bata sakte ho ki train kab chalti ya rukti hai. Lekin seedhe track par steady speed par tumhe lag sakta hai ki woh khadi hai. Tum velocity ko nahi, balki usmein change ko mehsoos karte ho. Velocity kitni jaldi badalti hai, yeh naapne ke liye hum average acceleration use karte hain.

\begin{aligned} average acceleration \\ = \frac{velocity mein change}{time interval} \end{aligned}

(4.3a)

a = \frac{v_{final} - v_{initial}}{time interval}

(4.3b)

Agar pehle wale instant $t_{1}$ par velocity $u$ hai aur baad wale instant $t_{2}$ par $v$ , to yeh ban jaata hai

a = \frac{v - u}{t_{2} - t_{1}}

(4.3c)

jahan

$a$: average acceleration
$u$: pehle wale instant par velocity
$v$: baad wale instant par velocity

Definition

Average acceleration

Kisi object ki velocity per unit time kitni badalti hai: velocity mein change ko usmein lage time se divide karo. Iski SI unit metre per second squared hai.

Acceleration ki SI unit metre per second per second hai, jise $m s^{- 2}$ ya m/s² likhte hain. $2 m s^{- 2}$ acceleration ka matlab hai ki velocity har second $2 m s^{- 1}$ badalti hai.

Displacement aur velocity ki tarah, acceleration ki bhi direction hoti hai. Seedhi line par, jab object ki speed badh rahi hoti hai, to uska acceleration usi taraf point karta hai jis taraf velocity. Jab woh dheema ho raha hota hai, to uska acceleration ulti taraf point karta hai aur isliye uska sign ulta hota hai (Fig. 4.4). Roz ki bolchaal mein dheema hone ko deceleration kehte hain; physics mein yeh bas motion ke against acceleration hai.

3/3Gaps ghatte hain; acceleration velocity ke opposite point karta hai.

Fig. 4.4Speed badhna: acceleration velocity ke saath. Dheema hona: acceleration uske against.NCERT Fig. 4.8 · p. 54

Sadak par ek chhoti van right ki taraf munh kiye khadi hai aur uske upar ek velocity arrow right ki taraf point karta hai. Uske left mein dots ek-ek second ke gap par uski positions dikhate hain. Step 1, speed badhna: dots ke beech ke gaps badhte hain aur van ke neeche ek dashed acceleration arrow right ki taraf point karta hai, velocity wali taraf hi. Step 2, steady velocity: gaps barabar hain aur acceleration par zero likha hai. Step 3, dheema hona: gaps ghatte hain aur acceleration arrow left ki taraf point karta hai, velocity ke opposite.

Velocity size mein, direction mein, ya dono mein badal sakti hai, aur inmein se har ek acceleration hai. Section 4.4.1 mein tum ek aisi motion se miloge jismein speed kabhi nahi badalti, sirf direction badalti hai, aur phir bhi acceleration hota hai.

Activity 4.2NCERT Activity 4.2 · p. 55

Vehicles kitni jaldi speed pakadte hain?

Tumhe chahiye

internet access ya koi motoring magazine
ek calculator

Pehle guess karo

Tumhe kya lagta hai, rest se

100 k m h^{- 1}

tak kiska average acceleration sabse zyada hoga?

Saamaan se bhara goods truckEk family hatchbackEk electric sports car

Car banane wali companies aksar batati hain ki car ko rest se $100 k m h^{- 1}$ tak jaane mein kitna time lagta hai. Teen-chaar alag vehicles ke liye yeh time dhoondho, jaise ek chhoti hatchback, ek SUV, ek electric car aur ek sports car.
Final speed ko metres per second mein badlo: $100 \times \frac{5}{18} \approx 27.8 m s^{- 1} .$
Har vehicle ke liye $27.8 m s^{- 1}$ ko bataye gaye time se divide karo. 12.5 s ke bataye gaye time ke liye average acceleration ka magnitude hai $27.8 \div 12.5 \approx 2.2 m s^{- 2} .$

Table 4.3

Vehicle	0 se 100 km/h tak ka time (s)	Average acceleration (m/s²)

Tumhari entries apne aap save hoti hain.

Example 4.3NCERT Example 4.3 · p. 55

City traffic mein ek autorickshaw

Ek autorickshaw seedhi sadak par $18 k m h^{- 1}$ se chal raha hai. Aage signal green hote hi driver throttle kholta hai aur 6 s mein auto $45 k m h^{- 1}$ tak pahunch jaata hai. Kuch der woh aise hi chalta hai; phir ek gaay sadak par aa jaati hai aur driver brake lagata hai, aur auto 2.5 s mein ruk jaata hai. Average acceleration nikaalo (a) speed badhate samay aur (b) brake lagate samay.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Ek surprise suno: sadak par sabse tez cheez ka acceleration sabse kam ho sakta hai. Seedhe track par steady $120 k m h^{- 1}$ se chalti express train ka acceleration zero hai, jabki signal se dheere-dheere nikalte scooter ka acceleration kaafi zyada ho sakta hai. Acceleration naapta hai ki velocity kitni jaldi badal rahi hai, yeh nahi ki velocity kitni badi hai.

Is chapter mein hum sirf constant acceleration wali motion dekhenge: velocity har barabar time ke hisse mein, chahe woh kitna bhi chhota ho, same amount se badalti hai. Example 4.4 bilkul aisi hi motion dikhata hai. Jaise velocity ek instant par batayi ja sakti hai, waise hi acceleration bhi; instantaneous acceleration se tum aage ki classes mein miloge.

Example 4.4NCERT Example 4.4 · p. 56

Pul se giraya gaya patthar

Ek patthar ko pul ki railing ke upar se rest se chhoda jaata hai. Chhodne wale point se naapte hue, neeche ko positive lekar, har aadhe second par uski velocity record ki jaati hai (Table 4.4). Har aadhe second ke interval mein average acceleration nikaalo. Kya yeh constant hai? Yeh kis taraf point karta hai?

Table 4.4Girte patthar ki velocity

Time (s)	0	0.5	1.0	1.5	2.0
Velocity (m/s)	0	4.9	9.8	14.7	19.6

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Freely girte object ka yeh constant acceleration acceleration due to gravity hai, jise $g$ likhte hain. Earth ki surface ke paas $g \approx 9.8 m s^{- 2}$ , aur koi asli girta object tab tak yahi acceleration rakhta hai jab tak air resistance kam ho. Release point ko origin aur "neeche" ko positive lena humara apna faisla tha; isse bas har number positive raha. Koi bhi origin aur koi bhi direction chalegi, bas problem ki pehli line se aakhri line tak wahi choice rakho. (Yo-yo activity mein bhi humne neeche ko positive liya tha; sadak par hum aam taur par chalne ki direction lete hain.)

Quick check

4 mein se 1

Seedhe expressway par steady

90 k m h^{- 1}

se chalti car ka acceleration bada hai, kyunki woh tez chal rahi hai.

SahiGalat

Answer dekho

Answer Galat

Acceleration naapta hai ki velocity kitni tezi se badalti hai. Steady velocity, chahe kitni bhi badi ho, ka matlab zero acceleration hai.

4.2 Motion ka Graphical Representation

Readings ki table motion ko bilkul theek describe karti hai, lekin ek nazar mein samajhna mushkil hai. Graph unhi readings ko ek picture mein badal deta hai, aur aankh pictures samajhne mein bahut achhi hai: koi mod, koi flat hissa ya koi steep chadhaai turant dikh jaati hai. Is section mein aage tum graph se seedhe velocities aur distances bhi naapoge. Tumne mathematics mein line graphs banaye hain; yahan hum motion ki ek quantity, position ya velocity, ko time ke against plot karte hain.

4.2.1 Graph plot karna

Chalo Table 4.5 ki readings se seedhi sadak par ek cyclist ki motion plot karte hain.

Table 4.5Seedhi sadak par ek cyclist ki position

Time (s)	0	1	2	3	4	5	6
Position (m)	0	5	10	15	20	25	30

Activity 4.3NCERT Activity 4.3 · p. 57

Position–time graph banao

Tumhe chahiye

graph paper
ek nukeeli pencil aur ek ruler

Pehle guess karo

Plot karne se pehle readings dekho. Tumhe graph ki kaisi shape ki ummeed hai?

Ek seedhi lineEk curve jo aur steep hoti jaati haiEk horizontal line

Graph paper ki sheet ke neeche left ke paas right angle par do lines banao: ek horizontal x-axis aur ek vertical y-axis. Yeh origin O par milti hain.
Tay karo ki kis axis par kya jaayega. Time woh quantity hai jise hum apni marzi se chunte hain, isliye woh x-axis par jaata hai; position y-axis par upar jaati hai. Har axis par quantity aur uski unit likho.
Aise scales chuno jo readings ko sheet ke zyadatar hisse par phaila dein. Yahan x-axis par har second ke liye 2 cm aur y-axis par har 5 m ke liye 1 cm achha chalta hai. Barabar steps par 1 s, 2 s, … aur 5 m, 10 m, … mark karo.
Readings ka har pair plot karo. (2 s, 10 m) ke liye x-axis par 2 s dhoondho, seedhe upar jao jab tak y-axis ke 10 m ke level par na pahuncho, aur wahan ek dot lagao. Pehli reading, (0 s, 0 m), khud origin hai.
Jab saari readings plot ho jaayein, dots ko ek smooth line se jodo; agar woh ek seedhi qatar mein hain to ruler use karo.

4/4Points origin se guzarti seedhi line par hain.

Fig. 4.5Axes, scales, points, line: graph banane ke chaar stages.NCERT Fig. 4.11 · p. 57

Graph paper ki ek sheet jis par seconds mein ek horizontal time axis aur metres mein ek vertical position axis origin O par milte hain. Step 1 mein sirf axes aur unke labels hain. Step 2 mein scale aata hai: time axis par 1 se 6 seconds aur position axis par upar 5 se 30 metres. Step 3 mein saat readings dots ki tarah plot hoti hain, aur dashed guide lines dikhati hain ki 2 seconds aur 10 metres wala point kaise milta hai. Step 4 dots ko origin se guzarti seedhi line se jodta hai.

Example 4.5NCERT Example 4.5 · p. 58

Chal padta scooter

Ek scooter signal par rest se shuru hota hai aur seedhi sadak par speed badhata hai. In readings se position–time graph plot karo aur uski shape describe karo.

Time (s)	0	1	2	3	4	5	6
Position (m)	0	2	8	18	32	50	72

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Fig. 4.6Scooter ka position–time graph upar ki taraf mudta hai kyunki woh har second zyada distance cover karta hai.NCERT Fig. 4.12 · p. 58

Metres mein position, 0 se 80 tak, ka seconds mein time, 0 se 6 tak, ke against graph. Time 0 se 6 seconds ke liye 0, 2, 8, 18, 32, 50 aur 72 metres par saat dots ek smooth curve se jude hain jo origin par flat shuru hoti hai aur aur-aur steep hoti jaati hai.

4.2.2 Position–time graphs

Position–time graph ban jaane ke baad uski shape motion ki kahani batati hai. Fig. 4.7 teen basic shapes dikhata hai.

3/3Har agle second mein bada rise (3 m, phir 9 m): velocity badh rahi hai.

Fig. 4.7Flat: rest mein. Seedhi aur dhalaan wali: constant velocity. Upar ki taraf mudti: speed badh rahi hai.NCERT Fig. 4.13 · p. 59

Ek hi set of axes, 0 se 40 metres tak position ko 0 se 6 seconds tak time ke against. Step 1 mein 25 metres par ek horizontal line highlight hoti hai, jis par at rest at 25 m likha hai. Step 2 mein origin se 6 seconds par 30 metres tak ek seedhi line highlight hoti hai, jis par constant velocity likha hai, aur do chhote triangles dikhate hain ki 1 aur 2 s ke beech ke second mein 5 m ka rise hai aur 4 aur 5 s ke beech bhi utna hi. Step 3 mein origin se ek curve highlight hoti hai jo steep hoti jaati hai, jis par speeding up likha hai, aur triangles dikhate hain ki 1 aur 2 s ke beech sirf 3 m ka rise hai lekin 4 aur 5 s ke beech 9 m. Jin lines ki baat nahi ho rahi, woh halki rehti hain.

Horizontal line ka matlab hai ki position nahi badalti, isliye object rest mein hai. Dhyaan do ki woh origin se 25 m door rest mein hai, origin par nahi.
Seedhi dhalaan wali line ka matlab hai barabar times mein barabar displacements, isliye velocity constant hai.
Steep hoti jaati curve ka matlab hai ki har second ka displacement badhta rehta hai, isliye velocity badh rahi hai: motion accelerated hai.

Position–time graph sirf yeh nahi batata ki har instant par object kahan hai. Yeh yeh bhi batata hai ki position kitni tezi se badal rahi hai. Agli activity dikhati hai kaise.

Activity 4.4NCERT Activity 4.4 · p. 59

Graph se velocity

Tumhe chahiye

Activity 4.3 wala tumhara graph
ek ruler aur ek pencil

Pehle guess karo

Agar tum usi seedhi line par do alag points chunte, to kya same answer milta?

Nahi, answer chune gaye points par depend karta haiSirf tab jab dono points theek 1 s ke gap par honHaan, koi bhi do points same answer dete hain

Activity 4.3 wale apne graph par line ke do points chuno: 2 s par A aur 5 s par B (Fig. 4.8).
A se time axis ke parallel ek line banao. B se position axis ke parallel ek line banao. Yeh C par milti hain aur ek right-angled triangle ABC banati hain.
Side CB position mein change hai, $s_{2} - s_{1}$ . Side AC time mein change hai, $t_{2} - t_{1}$ . Inhe graph se padho: $C B = 25 - 10 = 15 m$ aur $A C = 5 - 2 = 3 s$ .
CB ko AC se divide karo.

3/3Slope = rise ÷ run = $15 m \div 3 s = 5 m s^{- 1} .$

Fig. 4.8Position–time line ka slope velocity hai.NCERT Fig. 4.14 · p. 59

Cyclist ka graph, 0 se 30 metres tak position ko 0 se 6 seconds tak time ke against, origin se guzarti ek seedhi line hai. 2 seconds aur 10 metres par point A aur 5 seconds aur 25 metres par point B marked hain. Step 1 line aur do points dikhata hai. Step 2 ek dashed right-angled triangle banata hai: A se C tak ek horizontal side jis par 3 s likha hai aur C se upar B tak ek vertical side jis par 15 m likha hai. Step 3 result jodta hai: slope barabar 15 m divided by 3 s, yaani 5 metres per second.

v_{av} = \frac{C B}{A C} = \frac{s_{2} - s_{1}}{t_{2} - t_{1}}

Definition

Line ka slope

Graph par seedhi line kitni steep hai: y-quantity mein change ko x-quantity ke matching change se divide karo. Yeh batata hai ki x-quantity badhne par y-quantity kitni tezi se badhti hai.

To position–time graph ka slope velocity hai. Zyada steep line ka matlab zyada velocity, aur horizontal line ka slope zero hota hai, jiska matlab rest hai. Curved graph ka slope point-point par badalta hai. Curve se kisi ek instant ki velocity nikaalne ke liye tangent line chahiye, jiske baare mein tum aage ki classes mein seekhoge.

Example 4.6NCERT Example 4.6 · p. 60

Delivery van ka graph padhna

Fig. 4.9 seedhi gali par ek delivery van ka position–time graph hai. Van ki motion describe karo.

Fig. 4.9Delivery van ka position–time graph.NCERT Fig. 4.15 · p. 60

Metres mein position, 0 se 80 tak, ka seconds mein time, 0 se 10 tak, ke against graph. Ek seedhi line origin se 4 seconds par 30 metres tak upar jaati hai, 7 seconds tak 30 metres par flat rehti hai, phir zyada steep seedhi line mein 10 seconds par 60 metres tak upar jaati hai.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 4.7NCERT Example 4.7 · p. 60

Kaunsa cyclist zyada tez hai?

Fig. 4.10 do cyclists, P aur Q, ke position–time graphs dikhata hai jo seedhi sadak par ek hi taraf chal rahe hain. Kiski velocity zyada hai, aur kitni zyada?

Fig. 4.10Do cyclists ke position–time graphs.NCERT Fig. 4.16 · p. 60

Metres mein position, 0 se 60 tak, ka seconds mein time, 0 se 10 tak, ke against graph. Do seedhi lines origin se shuru hoti hain. Solid line P 10 seconds par 60 metres tak pahunchti hai; dashed line Q, kam steep, 10 seconds par 40 metres tak pahunchti hai.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Quick check

4 mein se 1

Position–time graph par time axis ke parallel seedhi line ka matlab hai ki object

steady velocity se chal raha hairest mein haispeed badha raha hai

Answer dekho

Answer (B) rest mein hai

Har instant par position same hai, isliye object chal nahi raha. Steady, non-zero velocity se dhalaan wali seedhi line milti.

4.2.3 Velocity–time graphs

Velocity–time graph mein velocity y-axis par upar aur time x-axis par plot hota hai, aur ise Activity 4.3 ki tarah hi banate hain. Table 4.6 teen cars ki velocities deta hai, har ek seedhi sadak par.

Table 4.6Teen cars ki velocitiesNCERT Tables 4.5 aur 4.6 · p. 61

Time (s)	0	5	10	15	20
Car A (m/s)	12	12	12	12	12
Car B (m/s)	0	4	8	12	16
Car C (m/s)	16	12	8	4	0

2/3Velocity har 5 s mein $4 m s^{- 1}$ badhti hai: motion ki direction mein constant acceleration.

Fig. 4.11Horizontal: constant velocity. Upar jaati: speed badh rahi hai. Neeche girti: dheema ho raha hai.NCERT Fig. 4.17 · p. 61

Ek hi set of axes, 0 se 16 metres per second tak velocity ko 0 se 20 seconds tak time ke against. Step 1 mein car A highlight hoti hai, 12 metres per second par ek horizontal line, jis par steady likha hai. Step 2 mein car B highlight hoti hai, 0 seconds par 0 se 20 seconds par 16 metres per second tak upar jaati seedhi line, jis par speeding up likha hai. Step 3 mein car C highlight hoti hai, 0 seconds par 16 metres per second se 20 seconds par 0 tak girti dashed seedhi line, jis par slowing down likha hai. Baaki lines halki rehti hain.

Car A ka graph horizontal line hai: uski velocity kabhi nahi badalti, isliye uska acceleration zero hai. Car B ka graph zero se upar jaati seedhi line hai. Uski velocity har 5 s mein same $4 m s^{- 1}$ badhti hai: motion ki direction mein constant acceleration. Car C ki line har 5 s mein $4 m s^{- 1}$ girti hai: car rukne tak motion ke against constant acceleration.

Velocity–time graph ka slope

Activity 4.4 ka rise-over-run idea is naye tarah ke graph par lagao. Ab rise velocity ka change hai aur run time ka change, isliye unka ratio acceleration hai. Car B ke liye, 5 s aur 15 s ke beech velocity $4 m s^{- 1}$ se $12 m s^{- 1}$ tak badhti hai:

\begin{aligned} a & = \frac{(12 - 4) m s^{- 1}}{(15 - 5) s} \\ = 0.8 m s^{- 2} \end{aligned}

Car C ke liye yahi steps $a = - 0.8 m s^{- 2}$ dete hain, jahan minus sign batata hai ki acceleration velocity ke against point karta hai. Car A ki line ka slope zero hai, isliye uska acceleration zero hai.

Velocity–time graph ke neeche ka area

Ab graph line aur time axis ke beech ka area dekho. Car A ke liye 0 s aur 5 s ke beech yeh region ek rectangle hai (Fig. 4.12). Iski height velocity hai, $12 m s^{- 1}$ , aur iski width time hai, 5 s. Inka product, 60 m, theek utna hai jitna car A un 5 seconds mein travel karti hai.

Yahi baat har velocity–time graph ke liye sach hai, uski shape chahe jo ho: kisi bhi time ke hisse mein, graph aur time axis ke beech ghira area displacement hai. Car B ke liye 5 s se 15 s tak region rectangle nahi hai, lekin tum use do tukdon mein baant sakte ho. Neeche ka rectangle 10 s chauda aur $4 m s^{- 1}$ uncha hai, jo 40 m deta hai. Upar ke triangle ka base 10 s aur height $12 - 4 = 8 m s^{- 1}$ hai, isliye uska area $\frac{1}{2} \times 10 \times 8 = 40 m$ hai. 5 s aur 15 s ke beech car B ka displacement 40 m + 40 m = 80 m hai.

3/35 s se 15 s tak displacement = 80 m.

Fig. 4.12Velocity–time graph ke neeche ka area = displacement.NCERT Fig. 4.18 · p. 62

0 se 16 metres per second tak velocity ko 0 se 20 seconds tak time ke against. Step 1 mein car A ki 12 metres per second par horizontal line hai, aur uske neeche 0 se 5 seconds tak ka rectangle shaded hai jis par 60 m likha hai. Step 2 mein car B ki upar jaati line hai, aur uske neeche 5 se 15 seconds tak ka region do hisson mein shaded hai: 4 metres per second uncha ek rectangle jis par 40 m likha hai aur uske upar ek triangle jis par 40 m likha hai. Step 3 total jodta hai: 40 m plus 40 m barabar 80 m.

To ek velocity–time graph do sawaalon ka jawab deta hai: velocity kitni tezi se badalti hai (slope padho) aur object kitni door jaata hai (area naapo). Neeche motion lab mein dono try karo.

InteractiveMotion lab

Ek interactive motion lab. Presets (steady, speeding up, braking) ya do sliders initial velocity u ko 0 se 20 metres per second aur acceleration a ko minus 4 se plus 4 metres per second squared tak set karte hain. Play dabane par 10 seconds ki motion chalti hai: ek car distance scale wali seedhi sadak par chalti hai, aur saath mein ek position-time graph aur ek velocity-time graph current time tak bante jaate hain. Velocity-time line ke neeche ka area shaded hota hai. Ek time slider se tum kisi bhi instant par ruk sakte ho. Ek readout tumhare numbers ke saath v = u + at aur s = ut + half a t squared nikaalta hai aur batata hai ki shaded area s ke barabar hai; braking mein yeh batata hai ki car kahan aur kab ruki.

Fig. 4.13Initial velocity

u

aur acceleration

a

chuno, Play dabao, aur dono graphs ko badhte dekho. Shaded area hamesha displacement ke barabar hota hai.

Quick check

3 mein se 1

Har velocity–time graph ko us motion se match karo jo woh dikhata hai.

Left mein koi item tap karo, phir right mein uska match.

Answer dekho

Answer

Time axis ke upar horizontal line : Constant velocity
Upar jaati seedhi line : Steadily speed badhna
Axis tak girti seedhi line : Dheema hokar ruk jaana
Time axis par hi padi line : Rest mein

Velocity–time graph ki height velocity hai aur uska slope acceleration. Axis par padi line ka matlab hai poore time zero velocity: object rest mein hai.

4.3 Constant Acceleration ke saath Seedhi Line mein Motion ki Kinematic Equations

Motion ko dekhne ke liye graphs achhe hain; use calculate karne ke liye equations aur bhi achhi hain. Constant acceleration ka ek kaam ka nateeja hai: kisi instant ke acceleration aur kisi time ke hisse par uske average mein koi fark nahi hota, isliye (4.3c) kisi bhi interval par sahi hai. Isse hum paanch quantities ko jod sakte hain: initial velocity $u$ , final velocity $v$ , acceleration $a$ , time interval $t$ aur displacement $s$ . Hum ghadi us instant par shuru karte hain, $t = 0$ , jab velocity $u$ hai.

DerivationPehli do equations derive karna

Time t ke baad velocity. Average acceleration ki definition (4.3c) mein $t_{1} = 0$ aur $t_{2} = t$ rakho. Tab $a = (v - u) / t$ , isliye $a t = v - u$ . Rearrange karne par milta hai

v = u + a t

(4.4a)

Ise $u$ aur $a$ do, aur yeh kisi bhi baad ke time $t$ par velocity de deti hai. Velocity–time graph par yeh ek seedhi line hai jo height $u$ se shuru hoti hai aur slope $a$ ke saath upar jaati hai (Fig. 4.14).

3/3Upar triangle: base $t$ , height $v - u = a t$ .

Fig. 4.14Line ke neeche ka area ek rectangle (

u t

) plus ek triangle (

\frac{1}{2} a t^{2}

) hai.NCERT Fig. 4.19 · p. 63

Bina numbers ka ek velocity-time graph. Ek seedhi line velocity axis par height u se shuru hoti hai aur time t par height v tak upar jaati hai. Step 1 line dikhata hai, jis par u, v, t aur slope a likhe hain. Step 2 height u ke neeche, width t ka rectangle shade karta hai, jis par u t likha hai. Step 3 uske upar ka triangle shade karta hai, jiska base t aur height v minus u hai, jo a t ke barabar hai, aur us par one half t times (v minus u) likha hai.

Time t ke baad displacement. Displacement 0 se $t$ tak is line ke neeche ka area hai. Ise height $u$ aur width $t$ ke ek rectangle mein, aur base $t$ aur height $v - u$ ke ek triangle mein baanto; (4.4a) se yeh height $a t$ hai.

\begin{aligned} s & = u t + \frac{1}{2} t (v - u) \\ = u t + \frac{1}{2} t (a t) \end{aligned}

s = u t + \frac{1}{2} a t^{2}

(4.4b)

Displacement s ke baad velocity. Kabhi-kabhi time pata nahi hota, isliye hume bina $t$ wali equation chahiye. (4.4a) ki dono sides ka square karo:

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

Aakhri do terms mein se $2 a$ bahar nikaalo: $2 u a t + a^{2} t^{2} = 2 a (u t + \frac{1}{2} a t^{2}),$ aur (4.4b) se bracket theek $s$ hai. To

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

(4.4c)

Yeh teen kinematic equations hain, jinhe equations of motion bhi kehte hain. Inhe paanch quantities mein se koi bhi teen do, aur yeh baaki do wapas de deti hain: ek minute baad train kahan hogi, ya girta nariyal zameen par pahunchte waqt kitni tez hai.

Example

Station se nikalti train

Ek local train platform paar karte waqt $2 m s^{- 1}$ se chal rahi hai. Phir woh 20 s tak constant $0.5 m s^{- 2}$ se speed badhati hai. 20 s ke end par uski velocity aur us time mein cover ki gayi distance nikaalo.

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Example 4.8NCERT Example 4.8 · p. 65

Brake lagati car kitni door jaati hai?

Ek car ke brakes use $- 5 m s^{- 2}$ ka constant acceleration dete hain. Brake lagane ke baad car kitni door jaati hai, agar woh (a) $36 k m h^{- 1}$ (b) $54 k m h^{- 1}$ se chal rahi thi?

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Real life meinNCERT Science aur Society ko Jodna · p. 65

Safe distance kyun rakhein?

Khatra dekhne wala driver turant brake nahi lagata. Lagbhag ek second tak (thake hone par ya phone par nazar daalne par aur zyada) gaadi full speed par chalti rehti hai: yeh thinking distance hai. Uske baad hi braking distance shuru hoti hai. Dono speed ke saath badhti hain, aur braking distance speed ke square ke saath badhti hai (Fig. 4.15).

2/220 m thinking + 40 m braking = 60 m.

Fig. 4.15Do guna speed, teen guna stopping distance (reaction time 1 s, brakes

- 5 m s^{- 2}

).NCERT Fig. 4.20 · p. 65

Metres mein, 0 se 60 tak, same scale par bane do horizontal bars. Har bar ka ek saada hissa thinking distance ke liye aur ek hatched hissa braking distance ke liye hai, yeh maan kar ki reaction time 1 second hai aur brakes minus 5 metres per second squared dete hain. Step 1 sirf 36 kilometres per hour ka bar dikhata hai: 10 m thinking plus 10 m braking, total 20 m. Step 2 72 kilometres per hour ka bar jodta hai: 20 m thinking plus 40 m braking, total 60 m.

Geeli ya bajri wali sadak par, ghise hue tyres ya kamzor brakes ke saath, aur bahut bhari loaded gaadi ke liye braking distance aur bhi lambi hoti hai. Isiliye truck ke peeche tum jo gap chhodte ho, woh tumhari speed aur kharab haalaat ke saath badhna chahiye. Ek naya idea hai vehicle-to-vehicle (V2V) communication: cars aur trucks radio se apni speed aur braking broadcast karte hain, taaki car apne driver ko kai gaadiyan aage hone wale achanak stop ki warning de sake. Kai deshon mein iske trials chal rahe hain, India mein bhi.

Quick check

4 mein se 1

Ek bus rest se

1.2 m s^{- 2}

ke constant acceleration se chalna shuru karti hai. 15 s baad uski velocity kitni hai, m/s mein?

m/s

Answer dekho

Answer 18 m/s

v = u + a t = 0 + 1.2 \times 15 = 18 m s^{- 1} .

4.4 Plane mein Motion

Ab tak sab kuch ek line par chala hai: one dimension mein motion. Kai motions ko describe karne ke liye do directions chahiye. Classroom mein tairta paper plane, carrom board ke kinare se takra kar lautta striker, ya ceiling fan ke blade ki tip socho. Yeh plane mein, yaani two dimensions mein, motions hain.

4.4.1 Uniform circular motion

Jab koi object circular path par chalta hai, to uski motion circular hoti hai. Ishaan park ke ek circular track par anticlockwise cycle chalata hai; track ka radius 35 m hai (Fig. 4.16).

1/3A se B: arc ke saath distance 55 m; chord ke saath displacement 49.5 m.

Fig. 4.16Circle par distance arc ke saath chalti hai; displacement seedhi chord leta hai.NCERT Fig. 4.22 · p. 66

Upar se dekha gaya 35 m radius ka circular track, jismein starting point A right mein, B upar aur C left mein hai. Rider anticlockwise jaata hai. Step 1, A se B tak quarter round: curved arc highlight hai aur ek dashed seedha arrow A ko B se jodta hai; distance 55 m, displacement 49.5 m. Step 2, A se C tak half round: distance 110 m, aur circle ke aar-paar seedha arrow 70 m ka displacement dikhata hai. Step 3, full round karke wapas A: distance 220 m aur displacement 0 m.

A se B tak chauthai raasta ghoomne mein Ishaan circumference ka ek-chauthai, 55 m, cover karta hai ( $π = 22 / 7$ lekar). Uska displacement seedhi chord AB hai, sirf lagbhag 49.5 m. Aadhe raaste par C par woh 110 m cover kar chuka hai aur A se ek diameter, 70 m, door hai. Ek full round ke baad usne poori circumference, $2 π R = 220 m$ , cover kar li hai, phir bhi uska displacement zero hai.

Agar ek round mein time $T$ lagta hai, to ek round par uski average speed circumference ko $T$ se divide karke milti hai:

v_{av} = \frac{2 π R}{T}

(4.5)

jahan

$R$: circle ka radius
$T$: ek full round ka time

Full round par uski average velocity zero hai, kyunki full round par uska displacement zero hai.

Example

Park ke chakkar

Ishaan ko 35 m wale track ke har round mein 44 s lagte hain. Nikaalo (a) ek round ke liye uski average speed (b) ek round ke liye uski average velocity (c) half round ke liye uski average speed aur average velocity (magnitude).

Pehle khud try karo. Phir solution ek-ek step karke kholo.

Ab maan lo Ishaan apni speed bilkul steady rakhta hai. Constant speed par circle ke around motion ko uniform circular motion kehte hain. Iski speed kabhi nahi badalti. Kya iski velocity bhi same rehti hai?

Definition

Uniform circular motion

Constant speed par circular path ke saath motion. Velocity ki direction har waqt badalti rehti hai, isliye motion accelerated hai.

ExampleSteady rate se ghoomte fan ke blade par ek point.

Shehar ke ek square block ke around gaadi chalane ki tulna ek circular road ke around chalane se karo (Fig. 4.17). Block par car har side ke saath seedhi jaati hai aur sirf chaar corners par direction badalti hai. Zyada aur chhoti sides wale block mein zyada turns lagenge, har ek halka. Circular road iski limit hai: usmein koi seedha hissa hai hi nahi, isliye velocity ki direction har instant badalti hai, chahe speedometer ki needle bilkul na hile.

3/3Ek point par laane par arrows barabar lambe hain lekin sab alag-alag taraf point karte hain: velocity badalti rehti hai.

Fig. 4.17Circle par constant speed: har velocity arrow ki length same hai lekin direction alag.NCERT Fig. 4.23 · p. 66

Upar se dekha gaya, anticlockwise jaati car ki velocity arrows ke saath. Step 1: shehar ka ek square block, har side par ek arrow; direction sirf 4 corners par badalti hai. Step 2: 8 barabar lambe arrows wali circular road, har arrow circle ko chhoota hai aur uske saath point karta hai, jis par turning at every point likha hai. Step 3: wahi 8 arrows copy hokar ek hi point se shuru hote hain, aur 8 alag directions mein point karte barabar arrows ka ek star banate hain, jis par same length, new direction likha hai.

Activity 4.5NCERT Activity 4.5 · p. 67

Chhod do!

Tumhe chahiye

ek marble (kanche ki goli)
chikne andar wala ek bada ring, jaise ek chauda plastic bangle ya plastic bottle se kaata gaya ring
ek chikni table ya farsh

Pehle guess karo

Marble ring ke andar tezi se chakkar laga rahi hai. Tum ring ko utha lete ho. Marble kis taraf jaati hai?

Seedhe aage, us line ke saath jis taraf woh us pal ja rahi thiWoh circle mein ghoomti rehti haiSeedhe bahar, centre se door

Ring ko table par flat rakho. Marble ko aise jhatko ki woh andar ki deewar ke saath gol-gol ghoome.
Ek-do rounds ke baad, marble ko chhue bina ring ko seedha upar utha lo.
Dekho marble kaunsa raasta leti hai. Ring ko alag-alag pal par utha kar kuch baar dohrao.
Baarish ke din bahar ek doosra test karo: doosre logon se door ek geela chhata ghumao, aur dekho ki boondein uske kinare se kis taraf nikalti hain.

Ring hatte hi marble seedhi line mein lurhak jaati hai. Woh wahi direction rakhti hai jo chhodne ke instant par uski thi, jo release point par tangent ke saath hai (Fig. 4.18). Paani ki boondein bhi yahi karti hain. Jab tak ring tha, uski deewar marble ko side se dhakelti rehti thi aur uska raasta modti thi; ring ke bina use koi nahi modta. Chalte object ko modne ke liye push kyun chahiye, yeh ek aage ke chapter ka topic hai.

2/2Marble tangent ke saath seedhi aage jaati hai.

Fig. 4.18Chhodne par marble release point par tangent ke saath nikalti hai.NCERT Fig. 4.24 · p. 67

Upar se dekha gaya ek ring jiske sabse neeche ke point par ek marble hai. Step 1: ring ke andar ek curved dashed arrow dikhata hai ki marble anticlockwise ghoom rahi hai. Step 2: ring utha liya gaya hai aur halka dikhaya gaya hai; marble ek seedhi dashed line ke saath right ki taraf lurhak gayi hai jo release point par circle ko chhooti hai, aur us par ring lifted, marble goes straight on likha hai.

Release point par ek aisi line banao jo circle ko bas wahin chhoo kar nikle, aur kahin nahi. Yeh us point par tangent hai, aur yahi theek marble ke nikalne ka raasta hai. Circular path ke har point par yahi sach hai: velocity hamesha tangent ke saath hoti hai, aur us taraf point karti hai jidhar object chal raha hai.

To kya steady $40 k m h^{- 1}$ par mod leti car accelerate kar rahi hai? Uska speedometer kehta hai ki kuch nahi badal raha. Lekin velocity mein direction bhi shaamil hai, aur direction har pal badal rahi hai; badalti velocity, definition se hi, acceleration hai (Section 4.1.4). Isliye uniform circular motion accelerated motion hai, chahe speed bilkul na hile. Tum ise mehsoos bhi kar sakte ho: tez mod par car ke passengers mod ke bahar ki taraf dabte hain.

Shayad hi koi asli raasta ek perfect circle ho jis par bilkul steady speed se chala jaaye: Earth ka orbit thoda sa oval hai, aur koi driver needle ko bilkul sthir nahi rakhta. Phir bhi physicists satellites, Moon, planets aur sadak ke modon ke liye pehle model ki tarah uniform circular motion use karte hain, aur corrections baad mein jodte hain.

Quick check

4 mein se 1

Ek ceiling fan steady rate se ghoomta hai. Ek blade ki tip par ek point ki

speed constant aur velocity constant haispeed constant hai lekin velocity badal rahi haispeed badal rahi hai aur velocity badal rahi hai

Answer dekho

Answer (B) speed constant hai lekin velocity badal rahi hai

Tip barabar times mein barabar arcs cover karti hai, isliye uski speed constant hai, lekin uski motion ki direction mudti rehti hai, isliye uski velocity badalti hai.

Recap

Summary aur key points

Position ek chune gaye reference point se distance aur saath mein direction hai; line par direction ek + ya − sign hai (Section 4.1.1).
Rest aur motion reference point ke hisaab se tay hote hain: badalti rehne wali position ka matlab motion; fixed position ka matlab rest.
Distance travelled poore path ki length hai; displacement position ka net change hai, direction ke saath. Iska magnitude kabhi distance se zyada nahi hota (Section 4.1.2).
Average speed = total distance ÷ time interval; average velocity = displacement ÷ time interval, $m s^{- 1}$ mein (Section 4.1.3).
Average acceleration = velocity mein change ÷ time interval, $m s^{- 2}$ mein; speed badhne par yeh velocity ke saath aur dheema hone par uske against point karta hai (Section 4.1.4).
Freely girte object ka neeche ki taraf constant acceleration $g \approx 9.8 m s^{- 2}$ hota hai.
Position–time graph par: horizontal line = rest, seedhi dhalaan wali line = constant velocity, slope = velocity (Section 4.2.2).
Velocity–time graph par: slope = acceleration aur line ke neeche ka area = displacement (Section 4.2.3).
Constant acceleration ke liye: $v = u + a t$ , $s = u t + \frac{1}{2} a t^{2}$ aur $v^{2} = u^{2} + 2 a s$ (Section 4.3).
Stopping distance = thinking distance + braking distance; braking distance speed ke square ke saath badhti hai.
Radius $R$ wale circle ke ek round mein distance $2 π R$ aur displacement zero hai; average speed $= 2 π R / T$ (Section 4.4.1).
Uniform circular motion mein speed constant hai lekin direction lagaataar badalti hai, isliye yeh accelerated hai; velocity tangent ke saath point karti hai.

Chalo explore kareinNCERT Aage ka Safar · p. 71

Try karne ke liye projects

Ghoomti disc. Cardboard ki disc ke centre se 7 cm door ek chhota star banao aur centre se 3 cm door waisa hi ek aur star. Disc ko pencil par ghumao, pehle dheere aur phir tez. Kaunsa star pehle dhundhla hota hai? Dono same time mein ek round lagate hain, to kaunsa zyada tez chal raha hai?
Tumhara phone ek accelerometer. Kai phones mein ek sensor hota hai jo bahut chhote accelerations naapta hai. Ek free sensor app (apne teacher se suggest karne ko kaho) se readings record karo, pehle phone farsh par rakh kar aur phir apni phaili hui hatheli par rakh kar. Hatheli wali readings kabhi poori zero kyun nahi hoti?
Scales matter karte hain. Example 4.5 ki scooter readings ko do sheets par bahut alag scales lekar plot karo. Curve zyada steep dikhti hai ya zyada flat? Phir ek graphing app se wahi readings plot karwao aur dekho ki woh apne axes kaise chunta hai.
Kisi mechanic se poochho. Pata karo ki geeli sadak, ghise tyres, bhaari load, kohra aur neend mein driver gaadi ki stopping distance ko kaise badalte hain. Jo seekho, use school assembly ke liye ek road-safety poster ya chhote skit mein badlo.

Apna NCERT exercise question dhoondo

Hamare practice questions ncert.ai ke liye likhe gaye hain aur NCERT exercises ko follow karte hain. Apni textbook ke question se match karne wala question dhoondo; uska answer uske saath hai.

Tumhari NCERT textbook mein	Yahan practice question
NCERT Exercises Q1	Practice Q1
NCERT Exercises Q2	Practice Q2
NCERT Exercises Q3	Practice Q3
NCERT Exercises Q4	Practice Q4
NCERT Exercises Q5	Practice Q5
NCERT Exercises Q6	Practice Q6
NCERT Exercises Q7	Practice Q7
NCERT Exercises Q8	Practice Q8
NCERT Exercises Q9	Practice Q9
NCERT Exercises Q10	Practice Q10
NCERT Exercises Q11	Practice Q11
NCERT Exercises Q12	Practice Q12
NCERT Exercises Q13	Practice Q13
NCERT Exercises Q14	Practice Q14
NCERT Exercises Q15	Practice Q15
NCERT Exercises Q16	Practice Q16
NCERT Aage ka Safar	Practice Q23
NCERT Aage ka Safar	Practice Q24

Quick check: MCQs

Ruko aur socho4 questions
Ruko aur socho3 questions
4.1.4 Average acceleration4 questions
4.2.2 Position–time graphs4 questions
Velocity–time graph ke neeche ka area3 questions
4.3 Constant Acceleration ke saath Seedhi Line mein Motion ki Kinematic Equations4 questions
4.4.1 Uniform circular motion4 questions

Glossary · 13

Key terms (English + Hindi)

acceleration due to gravityगुरुत्वीय त्वरणgurutviya tvaran: Earth ke paas freely girte object ka neeche ki taraf constant acceleration, $g \approx 9.8 m s^{- 2}$ .Chapter mein pehli baar yahan aaya →
average accelerationऔसत त्वरणausat tvaran: Velocity mein change ko time interval se divide karo; SI unit $m s^{- 2}$ .Chapter mein pehli baar yahan aaya →
average speedऔसत चालausat chaal: Object kul kitni door jaata hai, use lage time se divide karo.Chapter mein pehli baar yahan aaya →
average velocityऔसत वेगausat veg: Displacement ko time interval se divide karo; iski direction hoti hai.Chapter mein pehli baar yahan aaya →

displacementविस्थापनvisthapan: Do instants ke beech position ka net change: direction ke saath ek seedhi line wali distance.Chapter mein pehli baar yahan aaya →
distance travelledतय की गई दूरीtay ki gayi doori: Object jo poora path cover karta hai uski total length, direction chahe jo ho. Iska sirf magnitude hota hai.Chapter mein pehli baar yahan aaya →

kinematic equationsगति के समीकरणgati ke sameekaran: Constant acceleration ke liye equations $v = u + a t$ , $s = u t + \frac{1}{2} a t^{2}$ aur $v^{2} = u^{2} + 2 a s$ .Chapter mein pehli baar yahan aaya →

magnitudeपरिमाणparimaan: Kisi quantity ka size: uska number aur unit, bina direction ke.Chapter mein pehli baar yahan aaya →

reference pointसंदर्भ बिंदुsandarbh bindu: Ek fixed point, jise origin bhi kehte hain, jahan se positions naapi jaati hain.Chapter mein pehli baar yahan aaya →

slopeढालdhaal: Graph par line kitni steep hai: y-quantity mein change ÷ x-quantity mein change.Chapter mein pehli baar yahan aaya →

tangentस्पर्श रेखाsparsh rekha: Ek seedhi line jo circle ko theek ek point par chhooti hai.Chapter mein pehli baar yahan aaya →

uniform circular motionएकसमान वृत्तीय गतिeksamaan vrittiya gati: Constant speed par circle ke around motion; velocity ki direction badalti rehti hai.Chapter mein pehli baar yahan aaya →
uniform motionएकसमान गतिeksamaan gati: Seedhi line mein aisi motion jismein barabar time intervals mein barabar distances cover hoti hain, yaani constant speed par.Chapter mein pehli baar yahan aaya →

Describing Motion Around Us (Hamare Aas-paas ki Motion ka Varnan): Class 9 Science Chapter 4 Hinglish mein

Is chapter mein aap kya seekhenge

4.1 Seedhi Line mein Motion

4.1.1 Position batana

4.1.2 Distance travelled aur displacement

4.1.3 Average speed aur average velocity

4.1.4 Average acceleration

4.2 Motion ka Graphical Representation

4.2.1 Graph plot karna

4.2.2 Position–time graphs

4.2.3 Velocity–time graphs

Velocity–time graph ka slope

Velocity–time graph ke neeche ka area

4.3 Constant Acceleration ke saath Seedhi Line mein Motion ki Kinematic Equations

4.4 Plane mein Motion

4.4.1 Uniform circular motion

Summary aur key points

Practice questions answers ke saath (NCERT “Revise karo, socho, behtar banao”)

Apna NCERT exercise question dhoondo

Quick check: MCQs

Key terms (English + Hindi)

Tum chapter ke end tak pahunch gaye