Critical Evaluation of Distance and Displacement
1. Key Definitions
- Distance: The total path covered by an object, irrespective of direction. (Scalar quantity)
- Displacement: The shortest straight-line distance from the initial to the final position. (Vector quantity: has both magnitude and direction)
2. Key Differences Between Distance and Displacement
| Aspect | Distance | Displacement |
|---|---|---|
| Definition | The total length of the path traveled. | The shortest straight-line distance from the initial to final position. |
| Nature | Scalar (only magnitude). | Vector (magnitude + direction). |
| Value | Always positive. | Can be positive, negative, or zero. |
| Dependence on Path | Depends on the actual path taken. | Only depends on initial and final positions. |
| Example | If a car moves in a circular path and returns to the starting point, distance is the total path covered. | Displacement in a full circle is zero because the starting and ending points are the same. |
3. Critical Analysis
(a) Common Misconceptions Among Students
- Confusion Between the Two Terms
- Students often think displacement and distance are always equal.
- Example: A car moving in a straight line will have equal distance and displacement, but in a circular motion, displacement may be zero.
- Understanding Zero Displacement in Motion
- Many students struggle with the concept that an object can move but still have zero displacement.
- Example: A runner completing a round lap (400m) in a stadium has distance = 400m but displacement = 0m.
- Graphical Representation Problems
- Drawing correct displacement vectors and differentiating them from distance can be challenging.
- Example: Understanding the shortest path on a curved trajectory.
- Significance in Physics Applications
- Students often fail to grasp why displacement is used in velocity calculations while distance is used for speed.
- Example: If a bus travels 100m east, 50m west, the total distance is 150m, but displacement is only 50m.
CBSE Previous Year Questions on Distance and Displacement (Last 10 Years)
1. Definition-Based Questions
Question (2023, 2019, 2017, 2015)
- Define distance and displacement. Give examples.
Solution:
- Distance: The total path traveled by an object. (Example: A car moving 10m forward and 5m back has a distance of 15m.)
- Displacement: The shortest path between the starting and ending points. (Example: In the same case, displacement is 5m.)
2. Conceptual Questions
Question (2022, 2018, 2016, 2013)
- A man walks 5m north, then 5m south. What is his total distance and displacement?
Solution:
- Distance = 5m + 5m = 10m
- Displacement = 0m (as he returns to the starting point)
3. Numericals on Distance and Displacement
Question (2021, 2019, 2014)
- A person moves 4m east and then 3m north. Find the magnitude of displacement.
Solution (Using Pythagoras Theorem):
d=(42+32)=16+9=25=5md = \sqrt{(4^2 + 3^2)} = \sqrt{16 + 9} = \sqrt{25} = 5m
Answer: 5m displacement
4. Direction-Based Questions
Question (2020, 2018, 2016)
- A cyclist moves 3km east, then 4km north. What is his total distance and displacement?
Solution:
- Distance = 3km + 4km = 7km
- Displacement =
(32+42)=9+16=25=5km\sqrt{(3^2 + 4^2)} = \sqrt{9 + 16} = \sqrt{25} = 5km
Answer: Distance = 7km, Displacement = 5km.
5. Application-Based Questions
Question (2019, 2015, 2012)
- A ball is dropped from a height of 20m. It bounces back to 15m, then falls again to 10m, then rises to 5m before stopping. Find total distance and displacement.
Solution:
- Distance traveled: 20m (down) + 15m (up) + 15m (down) + 10m (up) + 10m (down) + 5m (up) + 5m (down) = 80m
- Displacement: Final position is 0m from the initial position, so 0m displacement.
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