Distance (āĻĻā§ā§°āĻ¤ā§āĻŦ) & Displacement (āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§°)
Distance (āĻĻā§ā§°āĻ¤ā§āĻŦ)
What is Distance ?
Distance is the total length of the path travelled. āĻĻā§ā§°āĻ¤ā§āĻŦ āĻŽāĻžāĻ¨ā§ āĻšā§āĻā§ āĻāĻ˛āĻžā§° āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻĒāĻĨā§° āĻĻā§ā§°ā§āĻā§āĻ¯āĨ¤
Key Points (āĻŽā§āĻ˛ āĻŦāĻŋāĻˇāĻ¯āĻŧ)
- It is a scalar quantity : āĻ āĻāĻāĻž āĻ¸ā§āĻā§āĻ˛āĻžā§° ā§°āĻžāĻļāĻŋ
- Has only magnitude (no direction) : āĻā§ā§ąāĻ˛ āĻŽāĻžāĻ¨ āĻĨāĻžāĻā§ (āĻĻāĻŋāĻļ āĻ¨āĻžāĻ)
- Always positive : āĻ¸āĻĻāĻžāĻ¯āĻŧ āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ
Remember: Distance tells HOW MUCH you moved : Distance āĻŦā§āĻāĻžāĻ¯āĻŧ āĻāĻĒā§āĻ¨āĻŋ āĻāĻŋāĻŽāĻžāĻ¨ āĻĻā§ā§° āĻ’āĻ˛
Displacement (āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§°)
What is Displacement ?
Displacement is the shortest distance from initial to final position with direction. āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§° āĻŽāĻžāĻ¨ā§ āĻā§°āĻŽā§āĻāĻŖāĻŋ āĻ¸ā§āĻĨāĻžāĻ¨ā§° āĻĒā§°āĻž āĻļā§āĻˇ āĻ¸ā§āĻĨāĻžāĻ¨āĻ˛ā§āĻā§ āĻ¸ā§°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ āĻĻā§ā§°āĻ¤ā§āĻŦ (āĻĻāĻŋāĻļāĻ¸āĻš)āĨ¤
Key Points (āĻŽā§āĻ˛ āĻŦāĻŋāĻˇāĻ¯āĻŧ)
- It is a vector quantity. āĻ āĻāĻāĻž āĻā§āĻā§āĻā§° ā§°āĻžāĻļāĻŋ
- Has magnitude + direction. āĻŽāĻžāĻ¨ āĻā§°ā§ āĻĻāĻŋāĻļ āĻĻā§āĻ¯āĻŧā§āĻāĻž āĻĨāĻžāĻā§
- Can be positive, negative, or zero. āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ, āĻāĻŖāĻžāĻ¤ā§āĻŽāĻ āĻŦāĻž āĻļā§āĻ¨ā§āĻ¯ āĻš’āĻŦ āĻĒāĻžā§°ā§
Remember: Displacement tells WHERE you ended up. (Displacement āĻŦā§āĻāĻžāĻ¯āĻŧ āĻāĻĒā§āĻ¨āĻŋ āĻ’āĻ¤ āĻā§ āĻļā§āĻˇ āĻā§°āĻŋāĻ˛ā§)
Formula / Concept
For displacement in 2D (Pythagoras Theorem): D = √x2 + Y2
Used when motion is in two directions (like East & North) : āĻĻā§āĻāĻž āĻĻāĻŋāĻļāĻ¤ āĻāĻ¤āĻŋ āĻĨāĻžāĻāĻŋāĻ˛ā§ āĻāĻ āĻ¸ā§āĻ¤ā§āĻ° āĻŦā§āĻ¯ā§ąāĻšāĻžā§° āĻšā§
Practice Question
Q: A student walks 3 m East and then 4 m North. Find: i. Distance, ii. Displacement
Soln (Ans)
Distance = 3 + 4 = 7 m : āĻĻā§ā§°āĻ¤ā§āĻŦ = ā§ āĻŽāĻŋ
Displacement = √(3² + 4²) = 5 m (North-East direction) : āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§° = ā§Ģ āĻŽāĻŋ (āĻāĻ¤ā§āĻ¤ā§°-āĻĒā§āĻŦ āĻĻāĻŋāĻļāĻ¤)
Tip
- Distance = Total path : āĻĻā§ā§°āĻ¤ā§āĻŦ = āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻĒāĻĨ
- Displacement = Shortest path + Direction : āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§° = āĻ¸ā§°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ āĻĒāĻĨ + āĻĻāĻŋāĻļ
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Distance & Displacement – MCQs
1. What is distance ?
A. Shortest path B. Total path length C. Direction D. Speed
Ans: B. Total path length
Explanation: Distance is the complete path travelled, not the shortest path. āĻĻā§ā§°āĻ¤ā§āĻŦ āĻšā§āĻā§ āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻāĻ˛āĻž āĻĒāĻĨ, āĻ¸ā§°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ āĻĒāĻĨ āĻ¨āĻšāĻ¯āĻŧāĨ¤
2. What is displacement ?
A. Total path B. Speed C. Shortest path with direction D. Time
Ans: C. Shortest path with direction
Explanation:Displacement is the shortest distance between start and end with direction. āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§° āĻšā§āĻā§ āĻā§°āĻŽā§āĻāĻŖāĻŋ āĻā§°ā§ āĻļā§āĻˇ āĻ¸ā§āĻĨāĻžāĻ¨ā§° āĻŽāĻžāĻā§° āĻ¸ā§°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ āĻĻā§ā§°āĻ¤ā§āĻŦ (āĻĻāĻŋāĻļāĻ¸āĻš)āĨ¤
3. Distance is a ______ quantity.
A. Vector B. Scalar C. Both D. None
Ans: B. Scalar
Explanation: Distance has only magnitude, no direction → scalar. āĻĻā§ā§°āĻ¤ā§āĻŦā§° āĻā§ā§ąāĻ˛ āĻŽāĻžāĻ¨ āĻĨāĻžāĻā§, āĻĻāĻŋāĻļ āĻ¨āĻžāĻ → āĻ¸ā§āĻā§āĻ˛āĻžā§°āĨ¤
4. Displacement is a ______ quantity.
A. Scalar B. Vector C. None D. Both
Ans: B. Vector
Explanation: Displacement has magnitude + direction → vector. āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§°āĻ¤ āĻŽāĻžāĻ¨ āĻā§°ā§ āĻĻāĻŋāĻļ āĻĻā§āĻ¯āĻŧā§āĻāĻž āĻĨāĻžāĻā§ → āĻā§āĻā§āĻā§°āĨ¤
5. Distance always has ______.
A. Direction B. Magnitude only C. Both D. None
Ans: B. Magnitude only
Explanation: Distance only shows “how much,” not direction. āĻĻā§ā§°āĻ¤ā§āĻŦ āĻā§ā§ąāĻ˛ “āĻāĻŋāĻŽāĻžāĻ¨” āĻŦā§āĻāĻžāĻ¯āĻŧ, āĻĻāĻŋāĻļ āĻ¨ā§āĻĻā§āĻā§ā§ąāĻžāĻ¯āĻŧāĨ¤
6. Displacement has ______.
A. Only magnitude B. Only direction C. Both D. None
Ans: C. Both
Explanation: It shows both amount and direction of movement. āĻ āĻāĻ¤āĻŋā§° āĻĒā§°āĻŋāĻŽāĻžāĻŖ āĻā§°ā§ āĻĻāĻŋāĻļ āĻĻā§āĻ¯āĻŧā§āĻāĻž āĻĻā§āĻā§ā§ąāĻžāĻ¯āĻŧāĨ¤
7. Distance can be ______.
A. Negative B. Zero C. Always positive D. Both
Ans: C. Always positive
Explanation: Distance is never negative because it is length. āĻĻā§ā§°āĻ¤ā§āĻŦ āĻā§āĻ¤āĻŋāĻ¯āĻŧāĻžāĻ āĻāĻŖāĻžāĻ¤ā§āĻŽāĻ āĻ¨āĻšāĻ¯āĻŧ, āĻ āĻĻā§ā§°ā§āĻā§āĻ¯āĨ¤
8. Displacement can be ______.
A. Only positive B. Only negative C. Positive/negative/zero D. None
Ans: C. Positive/negative/zero
Explanation: Depends on direction; can be zero if start = end. āĻĻāĻŋāĻļ āĻ
āĻ¨ā§āĻ¸ā§°āĻŋ āĻ§āĻ¨āĻžāĻ¤ā§āĻŽāĻ/āĻāĻŖāĻžāĻ¤ā§āĻŽāĻ/āĻļā§āĻ¨ā§āĻ¯ āĻš’āĻŦ āĻĒāĻžā§°ā§āĨ¤
9. If a person returns to starting point, displacement is ______.
A. Zero B. Maximum C. Negative D. Positive
Ans: A. Zero
Explanation: Initial and final positions are same → displacement = 0. āĻā§°āĻŽā§āĻāĻŖāĻŋ āĻā§°ā§ āĻļā§āĻˇ āĻāĻā§ → āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§° = ā§ĻāĨ¤
10. If path is straight line, distance is ______ displacement.
A. Less than B. Equal to C. Greater than D. Zero
Ans: B. Equal to
Explanation: In straight motion, path = shortest path. āĻ¸ā§āĻāĻž āĻāĻ¤āĻŋāĻ¤ āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻĒāĻĨ = āĻ¸ā§°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ āĻĒāĻĨāĨ¤
11. Unit of distance is ______.
A. kg B. m C. s D. N
Ans: B. m
Explanation: SI unit is meter. SI āĻāĻāĻ āĻŽāĻŋāĻāĻžā§°āĨ¤
12. Unit of displacement is ______.
A. m B. kg C. s D. A
Ans: A. m
Explanation: Same as distance → meter. āĻĻā§ā§°āĻ¤ā§āĻŦā§° āĻĻā§°ā§ āĻāĻā§ → āĻŽāĻŋāĻāĻžā§°āĨ¤
13. Distance depends on ______.
A. Direction B. Path C. Time D. Speed
Ans: B. Path
Explanation: Longer path = more distance. āĻĒāĻĨ āĻĻā§āĻāĻ˛ āĻš’āĻ˛ā§ āĻĻā§ā§°āĻ¤ā§āĻŦ āĻŦā§āĻāĻŋāĨ¤
14. Displacement depends on ______.
A. Path B. Initial & final position C. Speed D. Time
Ans: B. Initial & final position
Explanation: Only start and end matter. āĻā§ā§ąāĻ˛ āĻā§°āĻŽā§āĻāĻŖāĻŋ āĻā§°ā§ āĻļā§āĻˇ āĻ¸ā§āĻĨāĻžāĻ¨ āĻā§ā§°ā§āĻ¤ā§āĻŦāĻĒā§āĻ°ā§āĻŖāĨ¤
15. Which can be zero ?
A. Distance B. Displacement C. Both D. None
Ans: B. Displacement
Explanation: Distance cannot be zero if movement happens, but displacement can. āĻāĻ˛āĻžāĻāĻ˛ āĻĨāĻžāĻāĻŋāĻ˛ā§ āĻĻā§ā§°āĻ¤ā§āĻŦ ā§Ļ āĻ¨āĻšāĻ¯āĻŧ, āĻāĻŋāĻ¨ā§āĻ¤ā§ āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§° ā§Ļ āĻš’āĻŦ āĻĒāĻžā§°ā§āĨ¤
Numerical MCQs
16. 5 m east + 5 m west, distance = ?
A. 0 B. 5 m C. 10 m D. 2 m
Ans: C. 10 m
Explanation: Total path = 5 + 5 = 10 m. āĻŽā§āĻ āĻĒāĻĨ = ā§Ģ + ā§Ģ = ā§§ā§Ļ āĻŽāĻŋ
17. Same case, displacement = ?
A. 0 B. 10 m C. 5 m D. 2 m
Ans: A. 0
Explanation: Start = End → displacement = 0. āĻā§°āĻŽā§āĻāĻŖāĻŋ = āĻļā§āĻˇ → āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§° = ā§Ļ
18. 3 m east + 4 m north, displacement = ?
A. 7 m B. 5 m C. 6 m D. 8 m
Ans: B. 5 m
Explanation: Use Pythagoras → √(3² + 4²) = 5 m. āĻĒāĻžāĻāĻĨāĻžāĻā§ā§°āĻžāĻ → √(3² + 4²) = ā§Ģ āĻŽāĻŋ
19. Distance in above case = ?
A. 5 m B. 7 m C. 3 m D. 4 m
Ans: B. 7 m
Explanation: Total path = 3 + 4 = 7 m. āĻŽā§āĻ āĻĒāĻĨ = ā§ āĻŽāĻŋ
20. Straight 10 m walk, displacement = ?
A. 0 B. 10 m C. 5 m D. 20 m
Ans: B. 10 m
Explanation: Straight line → displacement = distance. āĻ¸ā§āĻāĻž āĻĒāĻĨ → āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§° = āĻĻā§ā§°āĻ¤ā§āĻŦ
Must Remember : i. Distance = Total path travelled : āĻĻā§ā§°āĻ¤ā§āĻŦ = āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻĒāĻĨ, ii. Displacement = Shortest path + direction : āĻ¸ā§āĻĨāĻžāĻ¨āĻžāĻ¨ā§āĻ¤ā§° = āĻ¸ā§°ā§āĻŦāĻ¨āĻŋāĻŽā§āĻ¨ āĻĒāĻĨ + āĻĻāĻŋāĻļ