Position, Displacement and Velocity Vectors

Position Vector

A vector that extends from a reference point to the point at which particle is located is called position vector.

Let r be the position vector of a particle P located in a plane with reference to the origin O in x-y plane.

Position Vector
Position Vector

Displacement Vector

Displacement vector is that vector which tells how much and in which direction an object has changed its position in a given time interval.

Let an object moving in the x-y plane. Let it is at point P at any instant t₁ and at point Q at any later time t₂.

Displacement Vector
Displacement Vector

In ∆OPQ,

OP + PQ = OQ

PQ = OQ – OP

∆r = r₂ – r₁

If the position coordinate of point P and Q are (x₁, y₁) and (x₂, y₂) respectively, then

r₁ = x₁ i^ + y₁ j^

r₂ = x₂ i^ + y₂ j^

Displacement Vector ∆r = r₂ – r₁

∆r = (x₂ – x₁)i^ + (y₂ – y₁) j^

For Three Dimensions

∆r = (x₂ – x₁)i^ + (y₂ – y₁) j^ + (z₂ – z₁)k^

Velocity Vector

The rate of change of displacement of an object in a particular direction is called its velocity.

It is of two types.

(I) Average Velocity

It is defined as the ratio of the displacement and the corresponding time interval.

Average Velocity
Average Velocity

(II) Instantaneous Velocity

The velocity at an instant of time t is known as instantaneous velocity.

The average velocity will become instantaneous, if ∆t approaches to zero.

The instantaneous velocity is expressed as-

Instantaneous Velocity
Instantaneous Velocity

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