The document Position, Path length,Displacement and Speed and Velocity (Average and Instantaneous) Class 11 Notes | EduRev is a part of the Class 11 Course Physics For JEE.

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**Position**

Position can be understood as the location of an object with respect to a reference point. It is expressed as a **position vector.**

Shown below is the position of a cyclist with respect to a lamp post. Cyclist starts at the lamp post and goes to Position 1, 2, 3 and 4 respectively.

Position 1, P1→ = +3 units

Position 2, P2→ = +5 units

Position 3, P3→ = -2units

Position 4, P4→ = -6units**Path Length/Distance**

- The total length of the path covered by the moving object.
- It is dependent on the path chosen, thus for motion between two fixed points A and B we can have many different values of the distance traversed.
- It is a
**scalar quantity**, as the length of the path has no indication of the direction in it. - Its SI unit is meter (m) and its dimension is (L).
- The following image shows the distance covered by the same cyclist.

Path Length = 16 units = Distance

**Displacement**

- Shortest distance between the initial and final positions. It is a vector.
- Its magnitude is the minimum distance between the final and initial point and is directed from the initial position to the final position.
- For a particle moving along the x-axis, motion from one position x
_{1}to another position x_{2}, is displacement, Δx where,

Δx = x_{2 }- x_{1} - If the particle moves from x
_{1}= 4m to x_{2 }= 12 m, then Δx = (12m)-(4m) = +8m. The positive result indicates that the motion is in the positive direction. If the particle then returns to x = 4m, the displacement for the full trip is zero. The actual number of meters covered for the full trip is irrelevant, displacement involves only the original and final position.**Final Displacement, D→ = -6 units**

It is interesting to observe that the final displacement vector is the same as the final position vector. This is because,

**P1→ + P2→ + P3→ + P4→D→ = 3 + 2 - 7 - 4 = -6 units**

**General Formula of Displacement**

Displacement between two positions starting at P_{A}→ and ending at P_{B}→ is defined as −

**Displacement, D→ = PB→ - PA→**

For Example, in the figure below,

Displacement between position 2 and position 4,

D→ = P_{4}→ - P_{2}→ = -6 - (+5) = -11 units

**Distance and Displacement Relationship**

The magnitude of Displacement **may or may not** be equal to Distance.

For example, in the figure below,

Between **P1**→ and **P2**→ −

**Distance = 2 units**

**Magnitude of displacement = |+5 - (+3)| = 2 units**

Between **P1**→ and **P3**→ −

**Distance = 9 units**

**Magnitude of displacement = |-2 - (+3)| = 5 units**

Important Note:

- If the object doesn’t change direction during motion, distance is equal to magnitude of displacement. (as evident between P1→ and P2→)
If the object changes direction during motion, distance is always greater than displacement. (as evident between P1→ and P3→)

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