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1.1.14 · D5 · HinglishMeasurement, Vectors & Kinematics

Question bank — Average velocity vs instantaneous velocity

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1.1.14 · D5 · Physics › Measurement, Vectors & Kinematics › Average velocity vs instantaneous velocity

Shuru karne se pehle, do words jo hum baar baar use karenge, simple language mein:

  • Displacement = woh seedha arrow jahan se tum shuru hue wahan se jahan tum khatam hue tak (ek vector). Dekho Distance vs displacement.
  • Distance = us ulte-seedhe raaste ki total length jo tumne actually chala (ek plain positive number).

Average velocity displacement se banti hai; average speed distance se banti hai. Yeh split dimag mein rakho aur zyaadatar traps collapse ho jaate hain.

Sach ya jhooth — justify karo

Har prompt ek claim hai. True/false decide karo, phir reason do — sirf verdict se kuch nahi milega.

Agar ek car bilkul apne starting point par wapas aa jaaye, toh poori trip mein uski average velocity zero hogi.
Sach. Average velocity hai, aur ghar wapas aane ka matlab hai, isliye poora ratio zero hai chahe tum kitni bhi tez gaye ho.
Agar kisi interval mein average velocity zero hai, toh object kabhi hila hi nahi.
Jhooth. Zero average velocity ka sirf itna matlab hai ki net displacement zero hai. Object door ja ke wapas aa sakta hai; uski average speed (distance over time) tab bhi badi ho sakti hai.
Average speed, average velocity ki magnitude se chhoti ho sakti hai.
Jhooth. Path length hamesha straight-line displacement se kam se kam utni hi hoti hai, isliye average speed — kabhi chhoti nahi.
Ek ball jo seedhi upar pheki gayi aur same height par pakdi gayi, uski average velocity ki magnitude aur average speed equal hoti hai.
Jhooth. Ball direction reverse karti hai, isliye displacement (zero) distance (peak height ka do guna) se bahut chhota hai; lekin average speed positive hai.
Instantaneous velocity basically average velocity hi hai jo bahut chhote time par compute ki gayi ho.
Aadha sach, lekin "bahut chhota" wala word trap hai. Yeh ka limit hai — koi bhi finite window isse exactly nahi deta. Koi bhi real interval ab bhi fast aur slow moments ko mila deta hai.
Position–time graph par secant line aur tangent line ki slopes hamesha alag hoti hain.
Jhooth. Constant velocity wali motion mein graph ek seedhi line hoti hai, isliye har secant hi tangent hai — har jagah same slope. Dekho Position-time graphs.
Uniform acceleration ke liye, par average velocity, midpoint time par instantaneous velocity ke equal hoti hai.
Sach. Position graph ek parabola hai; uski chord slope, midpoint par tangent slope se match karti hai — yeh ek genuine theorem hai, koi coincidence nahi (dekho Equations of motion under uniform acceleration).
Non-uniform acceleration ke liye bhi, average velocity midpoint par instantaneous velocity ke equal hoti hai.
Jhooth. Midpoint rule quadratics ki special property hai. Cubic ya jerky motion mein chord slope generally kisi doosre interior time par tangent se match karti hai, midpoint par nahi.
Average velocity, start aur end velocities ka ordinary average hoti hai.
Generally jhooth. Yeh formula sirf uniform acceleration mein kaam karta hai, aur tab bhi yeh time ke hisaab se average karta hai. Sachi definition hamesha hi hai.
Agar do trips ke start aur end points same hain aur duration bhi same hai, toh unki average velocity bhi same hogi.
Sach. Average velocity sirf aur par depend karti hai, dono endpoints aur time se fix hain — beech ka ulta-seedha raasta irrelevant hai.

Error dhundo

Har line mein ek hidden flaw wali reasoning hai. Flaw ka naam batao.

"Car ki average velocity 60 km/h thi, toh halfway time par woh 60 km/h par chal rahi thi."
General motion ke liye galat — average velocity necessarily halfway time par nahi milti. Yeh sirf midpoint time par guaranteed hai aur sirf uniform acceleration ke under.
"Speed, velocity ka size hai, isliye average speed, average velocity ka size hona chahiye."
Error "size lena" aur "average karna" ka order swap kar deta hai. Average speed, instantaneous velocity ke sizes ka average karti hai (distance/time); size averaging ke baad leta hai — jab bhi direction reverse ho ye differ karte hain.
"Throw ke top par ball momentarily still hai, isliye wahan uski acceleration bhi zero hai."
Velocity aur uski rate of change ko confuse kar raha hai. Peak par hai, lekin gravity abhi bhi act kar rahi hai, isliye . Dekho Acceleration as derivative of velocity.
"Instantaneous velocity nikalne ke liye maine mein plug kiya."
Zero se divide nahi kar sakte. Instantaneous value ka limit hai; pehle ratio ko simplify karo (jab ho), phir use shrink hone do.
"Particle ne 200 m road cover ki, isliye uska displacement 200 m hai."
Distance aur displacement ko confuse kar raha hai. 200 m path length hai; displacement start-to-end ka seedha arrow hai aur chhota ho sakta hai (zero bhi).
"Maine har second speedometer readings ka average nikala aur use average velocity kaha."
Do errors hain: speedometer speed deta hai (direction nahi), aur readings ka average time samples ke hisaab se weight karta hai, displacement ke hisaab se nahi. Average velocity strictly hai.
"Do graph points ke beech chord ka slope wahan instantaneous velocity deta hai."
Chord (secant) slope interval par average velocity deta hai. Instantaneous velocity ek single point par tangent slope hai — woh limit jab chord ke ends ek saath slide hote hain. Dekho Slope and tangent in calculus.
"Kyunki object pehle speed up hua phir same speed par slow down hua, us stretch par uski average velocity woh common speed hai."
Direction aur displacement definition ko ignore kar raha hai. Average velocity, displacement over time hai; matching end speeds tumhe uske baare mein kuch nahi batata.

Why wale questions

"Why" ka answer mechanism se do, restatement se nahi.

Hum se displacement kyun divide karte hain, sirf displacement kyun report nahi karte?
Ek rate paane ke liye — position change per unit time — taaki alag durations ki trips comparable ho sakein. Ek bada displacement lambe time par ek slow trip ho sakti hai.
Average speed, se greater ya equal kyun honi chahiye?
Path length (speed ka numerator) chhote step lengths ka sum hai jo endpoints ko connect karne wale seedhe arrow se kabhi chhota nahi ho sakta — triangle-inequality wala idea.
ko shrink karna velocity estimate ki "blur" ko kyun kam karta hai?
Ek lamba window fast aur slow moments ko ek average mein mila deta hai, variation chhupa deta hai. Ek tiny window mein almost ek instant hota hai, isliye ratio wahan ki motion report karta hai na ki ek mixture ki.
Instantaneous velocity ek vector kyun hai jabki speedometer sirf ek number dikhata hai?
Kyunki yeh position vector ka derivative hai, isko direction inherit hoti hai — woh direction jahan object us instant ja raha hai. Speedometer sirf direction drop karta hai aur magnitude (speed) rakhta hai.
Jab do points merge hote hain toh secant line tangent kyun "ban jaati" hai?
Jab interval shrink hota hai, chord ek point par curve ke saath rest par pivot ho jaati hai; secant slopes ka limit precisely tangent slope hai, jo derivative hai.
Ek flat spot wala graph (horizontal tangent) kyun indicate kar sakta hai ki object momentarily rest par hai?
Flat tangent ki slope zero hoti hai, aur position–time graph par slope hi velocity hai — isliye wahan hai.
Average velocity beech ka path kitna bhi wild kyun ho, use ignore kyun karta hai?
Yeh sirf endpoints use karta hai ke zariye; journey ka interior formula mein kabhi nahi aata.

Edge cases

Woh scenarios jo definitions quietly cover karti hain — check karo ki tum agree karte ho.

Ek object 10 s tak perfectly still raha. Uski average aur instantaneous velocities kya hain?
Dono poori jagah zero hain: se milti hai, aur flat position graph ki tangent slope har jagah zero hai.
10 s tak rest mein raha object — uski average speed bhi zero hai?
Haan. Travel ki gayi distance zero hai, isliye distance over time bhi zero hai; yahan speed aur agree karte hain kyunki koi reversal nahi hai.
Ek particle right move karta hai, momentarily rukta hai, phir wapas aata hai. Exactly turning instant par kya hai?
Zero — position graph ki tangent wahan horizontal hai, chahe particle sirf momentarily rest par ho aur acceleration nonzero ho.
Position–time graph mein ek sharp corner (kink) par instantaneous velocity kya hai?
Undefined — left aur right tangent slopes disagree karte hain, isliye koi single derivative exist nahi karta. Physically iska matlab velocity mein instantaneous jump hai, jo real bodies avoid karte hain.
Ek round trip jo time leta hai, usmein (average speed)/ ratio kya hai?
Yeh undefined hai — jabki average speed positive hai, isliye ratio ek nonzero number ko zero se divide karta hai.
Agar displacement nonzero hai lekin object ne partway backtrack bhi kiya, toh average speed aur mein kya difference hai?
Average speed strictly badi hogi, kyunki backtracking path length add karta hai jo net displacement mein add nahi hoti.
Jab ek smooth graph par interval ke start aur end times ek doosre ke paas aate hain, toh average velocity kya approach karti hai?
Us shared instant par instantaneous velocity — yahi limiting process derivative ki exact definition hai.

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