Define displacement
Scenario
Aapko bheed wale raste se school jana padta hai jisme bahut saare turns hain. Lekin agar aapke paas helicopter hota, toh aap seedha udd kar chhat par pahunch jaate.
Yeh seedhi hawai udaan wali distance ko physics mein kya kehte hain?
Mental model
Displacement ek straight line shortcut hai initial point se final point tak.
Imagine karo ek rubber band ko apne start point aur end point ke beech stretch karna. Wo rubber band ka actual raasta nahi dekhta, bas dono points ke beech ka shortest distance pakadta hai. Isi shortest, seedhi line ko displacement kehte hain.
Explanation
Physics mein jab hum kisi object ki motion ko deeply analyze karte hain, toh sirf actual rasta (distance) matter nahi karta. Hamein yeh bhi dekhna hota hai ki aakhiri mein object apni initial jagah se kitna door hai. Is choti se choti seedhi line ko 'displacement' kehte hain.
Displacement ko dhyaan se samajhne ke liye ek example sochiye: aap ek point A se ghoom kar B tak jaate hain. Jo lamba rasta aapne liya, wo distance hai. Lekin agar aap A se B ke beech ek ruler rakh kar seedhi line kheenchte hain, toh us line ki length aapki displacement hogi. Displacement ko nikalte waqt hum raste ke mod ya curves ko ignore kar dete hain.
Kyunki displacement sirf initial (shuruati) aur final (aakhiri) point par depend karta hai, isliye iske saath direction batana bahut zaroori hota hai. Jaise, '5 km North'. Aisi quantities jisme magnitude (value) aur direction dono hon, unhe 'vector quantity' kehte hain.
Ek aur interesting baat displacement ke baare mein yeh hai ki yeh positive, negative ya zero bhi ho sakti hai. Agar aap chal kar wapas apne ghar aa gaye jahan se aapne shuru kiya tha, toh aapka starting aur ending point same ho gaya. Aise mein aapki displacement ekdum zero ho jayegi, bhale hi aapne 10 km kyun na chale hon.
Worked example
Problem: A car moves 3 km East and then 4 km North to reach its destination. Calculate the magnitude of its displacement.
- Path ek right-angled triangle banata hai. Shortest distance nikalne ke liye Pythagoras theorem use karte hain.
- Squares ko add karein.
- Final displacement ke liye square root lein.
Answer: 5 km
Problem: An athlete completes one round of a circular track of radius 50 m in 2 minutes. What is his displacement at the end of 2 minutes?
- Athletic track ke ek complete round ke baad, athlete apni starting position par wapas aa jata hai.
- Jab initial aur final position same hoti hai, toh shortest distance 0 hota hai.
Answer: 0 m
Key points
- Shortest distance: Displacement is the shortest straight-line distance from the initial position to the final position.
- Vector quantity: It is a vector quantity because it requires both magnitude (size) and direction.
- Can be zero: If the initial and final positions are the same, displacement is zero.
Common mistakes
- Adding segments like distance: Students often add 3 km and 4 km (to get 7 km) for displacement. Hamesha yaad rakhein ki displacement path length nahi hai, balki start to end ka straight line shortcut hai.
- Forgetting that direction matters: Distance ki tarah displacement ko simply add ya subtract nahi kiya ja sakta. Agar straight line mein opposite direction mein aayein toh negative karna padta hai.
Recall questions
- Is displacement a scalar or vector quantity?
- What is the shortest distance from the initial to the final position called?
- What is the displacement if a person returns exactly to their starting point?
Questions & answers
A farmer moves along the boundary of a square field of side 10 m in 40 s. What will be the magnitude of displacement of the farmer at the end of 2 minutes 20 seconds?
14.14 m
Approach: Total time is 140s. Number of rounds = 140/40 = 3.5 rounds. After 3 complete rounds, displacement is 0. The half round takes him to the diagonally opposite corner. Displacement = diagonal = sqrt(10^2 + 10^2) = sqrt(200) = 10 * sqrt(2) ≈ 14.14 m.
An object has moved through a distance. Can it have zero displacement? If yes, support your answer with an example.
Yes. If the object returns to its starting point, distance is non-zero but displacement is zero.
Approach: Define displacement as the shortest path from initial to final position. Use a circular track as an example.
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