Position, Path length,Displacement and Speed and Velocity (Average and Instantaneous) Class 11 Notes | EduRev

Physics For JEE

Class 11 : Position, Path length,Displacement and Speed and Velocity (Average and Instantaneous) Class 11 Notes | EduRev

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.
All you need of Class 11 at this link: Class 11

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 and Speed and Velocity (Average and Instantaneous) Class 11 Notes | EduRev
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 and Speed and Velocity (Average and Instantaneous) Class 11 Notes | EduRev


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.
    Position, Path length,Displacement and Speed and Velocity (Average and Instantaneous) Class 11 Notes | EduRev

    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 and Speed and Velocity (Average and Instantaneous) Class 11 Notes | EduRev

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 and Speed and Velocity (Average and Instantaneous) Class 11 Notes | EduRev

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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