Key Differences Between Distance and Displacement with Diagrams and Examples
Understanding the Difference Between Distance and Displacement is essential for mastering motion concepts in JEE Main Physics. Both terms often appear in kinematics questions, but they hold distinct meanings and determine how you approach problem-solving for straight-line or curvilinear motion.
In Physics, these quantities are used to describe how far and in what direction an object moves. Mistaking one for the other can lead to the wrong application of motion formulas and errors in numericals. This article explains their definitions, units, comparison, and practical use cases—all precisely tailored for JEE aspirants.
Definition and Concept: Distance vs Displacement
Distance is the total length of the actual path travelled by a body, without considering direction. It is always a non-negative scalar quantity. In contrast, Displacement refers to the shortest straight-line vector from the initial to the final position, including direction.
If a student walks 4 m east and then 3 m north, their distance covered is 7 m, but their displacement is the direct line between start and end, calculated using the Pythagoras theorem.
Key Differences Between Distance and Displacement
| Aspect | Distance | Displacement |
|---|---|---|
| Type | Scalar | Vector |
| Definition | Total path length travelled | Shortest straight-line change from start to end |
| Direction | No direction | Has direction |
| Possible values | Always positive or zero | Positive, negative, or zero |
| Magnitude | Can be greater than displacement | Never greater than distance |
| Symbol | d or s | Δx or →s |
| SI Unit | metre (m) | metre (m) |
- Distance adds up all movement, regardless of direction.
- Displacement only cares about the net change in position and direction.
Remember: in straight-line, one-way motion, distance and displacement values are equal. For a return journey, displacement can become zero while distance remains positive.
Formulas, SI Units, and Symbolic Representation
Distance (d) formula: add all path segments; Displacement (Δx) formula: final position minus initial position, with direction assigned.
- Distance: d = Sum of all path lengths
- Displacement: Δx = xfinal − xinitial
- Unit: Both measured in metres (m) in SI.
Example: If Meera walks 100 m forward and then 60 m backward, her total distance is 160 m. Her net displacement is 40 m forward.
Real-Life Example and Diagram: Distance and Displacement
Suppose a car travels around a rectangular park, covering each 200 m side and coming back to the starting point. The distance covered is 800 m. The displacement is zero, since the car ends up at the starting position.
- Running a full lap on a 400 m track: Distance = 400 m, Displacement = 0 m.
- Walking 3 m east and then 4 m north: Distance = 7 m, Displacement = 5 m (by Pythagoras).
In JEE Main, you'll encounter displacement vectors in questions on motion in one dimension and kinematics.
Solved Example: Applying Distance and Displacement in Kinematics
A student walks 6 m east, 8 m north, then stops. Calculate total distance and displacement.
- Total distance = 6 m + 8 m = 14 m
- Displacement = 10 m (use √(62 + 82) = 10 m)
Remember: Displacement uses shortest straight line, while distance is the sum of each leg of the walk.
In motion problems involving speed and velocity, scalar and vector distinctions are identical to those between distance and displacement.
Common Mistakes and Key Tips For JEE
- Assuming displacement is always positive. It can be zero or negative.
- Mixing up formulas—use displacement with velocity, distance with speed.
- For round-trip: displacement is zero, but distance is not.
- Avoid confusing magnitude (never negative) with sign (shows direction) for displacement.
- Carefully follow the sign convention in vector answers.
Practice similar numericals using kinematics mock tests and reference questions in JEE Main Physics question papers.
Practical Relevance and Related JEE Main Topics
A solid grasp of the Difference Between Distance and Displacement is vital for motion graphs, vectors, and calculating velocity or acceleration. It's essential in 2D motion and projectile motion problems.
- See difference between mass and weight for another scalar vs vector contrast.
- Explore units and measurement to ensure proper calculation of SI values.
- Master uniform and non-uniform motion to avoid traps on exam day.
- Deepen vector concept clarity at vectors in Physics.
Vedantu's JEE Physics resources clarify more such terms with trusted explanations and expert numericals, aligned strictly with the NCERT and the JEE Main syllabus.
FAQs on Difference Between Distance and Displacement Explained for JEE
1. What is the main difference between distance and displacement?
Distance refers to the total length of the path covered by an object, while displacement is the shortest straight-line distance from the initial to the final position.
Key points:
- Distance is a scalar quantity (no direction).
- Displacement is a vector quantity (has both magnitude and direction).
- Distance is always positive; displacement can be zero, positive, or negative.
- Displacement is always equal to or less than distance, never more.
2. Can distance be greater than displacement?
Yes, distance is always greater than or equal to displacement.
- If the path is straight without any turns, distance and displacement are equal.
- If the path is curved or involves turns, distance exceeds displacement.
- Displacement measures the shortest path, while distance measures the actual traveled path length.
3. Give one example showing difference between distance and displacement.
When a student walks 3 km east and then 4 km north, the distance traveled is 7 km (3 + 4), but displacement is 5 km in a straight line (by Pythagoras' theorem).
- This example demonstrates how distance can be more than displacement.
- Distance follows the path; displacement is the shortest route between start and end points.
4. What is the SI unit for distance and displacement?
The SI unit for both distance and displacement is the metre (m).
- Distance and displacement are measured using the same units: metre in SI.
- In some cases, kilometres (km) or centimetres (cm) may be used for convenience.
5. What are the formulas for distance and displacement?
The formula for distance is: Sum of all path segments traveled.
The formula for displacement is: Shortest straight-line change (final position - initial position), including direction.
- Distance: Add up all lengths traveled, regardless of direction.
- Displacement: Use vector subtraction (final position − initial position).
6. Is it possible to have zero displacement but non-zero distance? When?
Yes, displacement can be zero while distance is not zero if an object returns to its starting point.
- Example: Running a full lap around a track and ending at the starting point. Distance equals the length of the lap, but displacement is zero.
7. Why do distance and displacement have the same value in straight-line motion?
When an object moves in a straight line without changing direction, the distance traveled equals the displacement.
- Path followed is directly from start to endpoint.
- No deviation, so the shortest path and actual path are identical.
8. What is the difference between scalar and vector quantities in context of distance and displacement?
Distance is a scalar quantity (only magnitude), while displacement is a vector quantity (magnitude and direction).
- Scalars do not include direction.
- Vectors always specify both magnitude and the direction of movement.
9. How are distance and displacement related to speed and velocity?
Distance and displacement are the basis for speed and velocity calculations.
- Speed = Distance / Time (scalar)
- Velocity = Displacement / Time (vector)
- Speed uses the actual path; velocity uses the shortest path between two points.
10. What is an example of a situation where distance and displacement are equal?
If a person walks 100 m in a straight line from point A to point B without turning, both distance and displacement are 100 m.
- Both quantities are equal when there is no change in direction.
