Relative Velocity

Class XI Chapter 3

Relative Velocity

"The consideration of velocity of an object with respect to another object is said to be Relative Velocity."

Consider about two objects A and B moving in straight line with average velocities Va and Vb respectively.

Let the positions of the objects are at time t = 0 are Xa(0) and Xb(0) respectively.

After time T positions of the objects will be

Xa(t) = Xa(0) + Va.T

Xb(t) = Xb(0) + Vb.T

We know that 

Distance = Velocity x Time

Displacement from object A to object B 

= Xb(t) - Xa(t) = Xb(0) + Vb.T - Xa(t) - Va.T

or, Displacement from A to B = [Xa(0) - Xb(0)] + [Vb - Va].T

 The displacement A to B changes steadily by the amount Va - Vb.

This (Vb - Va) is also known as velocity of B relative to velocity of A.

Therefore, Relative velocity of B to A

Vba = Vb - Va.

Position - time graph of two objects with equal velocities.

When velocities are equal

Va = Va

Displacement from A to B = [Xa(0) - Xb(0)] 

The relative velocity will be zero and stay at constant distance.

Position - Time graph of two objects with unequal velocities.

When Va greater than Vb

The relative velocity of B to A will be Negative.

One graph is steeper than the other and they meet each other at a common point.

When Va and Vb have opposite sign.

 The magnitude of Vba will be greater than Va or Vb.

These three cases arises in Relative velocity.