Relative Velocity

Relative velocity is the velocity in 2 different frames. We might have experienced trees moving back while we are inside a moving vehicle. In reality, they are not, instead they are stationary and we are moving. Ourself and the trees are in 2 different frames. Let us say Frame-A is where we are in a car which is moving and the frame B is the stationary trees. Now since 2 frames are in a different state (one is moving another is stationary), we experience a relative change in the velocity. Suppose if we ask ourself, although we all are moving in a car we all feel within our self that we are stationary! This is because we all are in the same frame of movement. “The relative velocity is the velocity that the body-A would appear to an observer on the body-B and vice versa”. When we put it in a mathematical way, it is the vector difference between the velocities of two different bodies. In simple terms, the velocity of an object with respect to another object is called the relative velocity. If there are two moving objects A and B, the velocity of A with respect to B is the velocity that A would appear to have when observed from B.  Consider an object A moving with a velocity, VA and an object B moving with a velocity, VB in the same direction. The velocity of object A with respect to B or the relative velocity of object A is,

Relative velocity = velocity of the body A – velocity of the body B,

I, e vAB = vA – vB

vAB: relative velocity of the body A respect body B

vA: velocity of the body A

vB: velocity of the body B

Question: The river flows with a velocity 10 m/s. A man swims parallel to the river bank in the same direction as the flow of the river with a velocity of 2 m/s.

1. What is the relative velocity of the man?

2. What is the relative velocity of the man if he is moving against the flow of the river?


  1. 8 m/s

  2. 12 m/s