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.

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.

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^

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

It is of two types.

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

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-