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Distance and Displacement

Distance is the total length of the actual path travelled. Displacement is the shortest straight-line change in position from the initial point to the final point, with direction.

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Student-friendly explanation

Distance is a scalar quantity, so it has magnitude only. Displacement is a vector quantity, so direction matters. Distance can never be less than displacement in magnitude; they are equal only when motion is along a straight line without changing direction.

How to write this in exams

  1. 1

    Start with the exact idea

    Distance is the total length of the actual path travelled. Displacement is the shortest straight-line change in position from the initial point to the final point, with direction.

  2. 2

    Then show how to use it

    Write each part of the path for distance and add all lengths. For displacement, mark initial and final positions, choose direction, and find the straight-line change in position.

  3. 3

    Add one concrete example

    If a student walks 3 m east and then 4 m west, distance is 7 m, but displacement is 1 m west.

  4. 4

    Avoid this incomplete answer

    Writing displacement as 8 m in the worked example is wrong because 8 m is the total path length, not the net change in position.

Definition

Distance is the total length of the actual path travelled. Displacement is the shortest straight-line change in position from the initial point to the final point, with direction.

Example

If a student walks 3 m east and then 4 m west, distance is 7 m, but displacement is 1 m west.

Rule to remember

Distance = total path length. Displacement = final position minus initial position along a chosen direction. Magnitude of displacement is less than or equal to distance.

Memory hook

Distance follows the road; displacement points from start to finish.

Examples and method

Worked example

A girl walks 6 m north and then returns 2 m south. Distance = 6 + 2 = 8 m. Displacement = 4 m north, because her final position is 4 m north of the starting point.

Method to apply

Write each part of the path for distance and add all lengths. For displacement, mark initial and final positions, choose direction, and find the straight-line change in position.

Diagram support

A line or path diagram can show actual route length and a straight arrow from starting point to final point.

How CBSE asks it

Students may be given movements along a line or around a rectangle and asked to calculate distance and displacement separately.

Avoid common mistakes

Common confusion

Students often add directions like east and west as if both distance and displacement are the same type of quantity.

Common wrong answer

Writing displacement as 8 m in the worked example is wrong because 8 m is the total path length, not the net change in position.

Exam tip

For displacement, mark the starting point and ending point first; the actual route matters for distance, not for displacement.

Quick check

When can distance and displacement have the same magnitude?

Distance and displacement have the same magnitude when the object moves along a straight path in one direction without turning back.

Answer writing and exam use

1-mark answer

Distance is the total length of the actual path travelled. Displacement is the shortest straight-line change in position from the initial point to the final point, with direction.

2-mark answer

Distance is the total length of the actual path travelled. Displacement is the shortest straight-line change in position from the initial point to the final point, with direction. Distance = total path length. Displacement = final position minus initial position along a chosen direction. Magnitude of displacement is less than or equal to distance. If a student walks 3 m east and then 4 m west, distance is 7 m, but displacement is 1 m west.

3-mark answer

Distance is a scalar quantity, so it has magnitude only. Displacement is a vector quantity, so direction matters. Distance can never be less than displacement in magnitude; they are equal only when motion is along a straight line without changing direction. Distance = total path length. Displacement = final position minus initial position along a chosen direction. Magnitude of displacement is less than or equal to distance. A girl walks 6 m north and then returns 2 m south. Distance = 6 + 2 = 8 m. Displacement = 4 m north, because her final position is 4 m north of the starting point. Students may be given movements along a line or around a rectangle and asked to calculate distance and displacement separately. Writing displacement as 8 m in the worked example is wrong because 8 m is the total path length, not the net change in position.
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