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Position, Path Length & Displacement Notes | Study Physics For JEE - JEE

Document Description: Position, Path Length & Displacement for JEE 2022 is part of Physics For JEE preparation. The notes and questions for Position, Path Length & Displacement have been prepared according to the JEE exam syllabus. Information about Position, Path Length & Displacement covers topics like Position, Path Length/Distance, Displacement and Position, Path Length & Displacement Example, for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Position, Path Length & Displacement.

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Table of contents
Position
Path Length/Distance
Displacement
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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, Path Length & Displacement Notes | Study Physics For JEE - JEE
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.
    Position, Path Length & Displacement Notes | Study Physics For JEE - JEE


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 x1 to another position x2, is displacement, Δx where,
    Δx = x- x1
  • If the particle moves from x1= 4m to x= 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

    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 PA→ and ending at PB→ is defined as −

Displacement, D→ = PB→ - PA→


For Example, in the figure below,

Position, Path Length & Displacement Notes | Study Physics For JEE - JEE

Displacement between position 2 and position 4,

D→ = P4→ - P2→ = -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,

Position, Path Length & Displacement Notes | Study Physics For JEE - JEE

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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