physicscatalyst.com logo




Relative velocity




7. Relative velocity



  • Consider two objects A and B moving with uniform velocities vAand vB along two straight and parallel tracks.
  • Let xOAand xOB be their distances from origin at time t=0 and xAand xB be their distances from origin at time t.
  • For object A
    xA = xOA + vAt               (18)
    and for object B
    xB = xOB + vBt                (19)
    subtracting equation 18 from 19
    xB - xA = ( xOB - xOA ) + ( vB - vA) t                          (20)
  • Above equation 20 tells that as seen from object A , object B seems to have velocity ( vB - vA) .
  • Thus ( vB - vA ) is the velocity of object B relative to object A. Thus,
    vBA = ( vB - vA )                (21)
  • Similarly velocity of object A relative to object B is
    vAB = ( vA - vB )                (22)
  • If vB = vA then from equation 20
    xB - xA = ( xOB - xOA )
    i.e., two objects A and B stays apart at constant distance.
  • vA > vB then (vB - vA ) would be negative and the distance between two objects will go on decreasing by an amount ( vA - vB ) after each unit of time. After some time they will meet and then object A will overtake object B.
  • If vA and vB have opposite signs then magnitude of vBA or vAB would be greater then the magnitude of velocity of A or that of B and objects seems to move very fast.
  • In short
    Relative velocity Formula

Watch this tutorial for more information on Relative Velocity

Relative velocity Conceptual questions

A. A gun is mounted on a train roof .Train is travelling with the velocity v in north direction.A car is also moving on a parallel track with train with velocity w in north direction.Two bullet are fired from the muzzle of the gun . Take north as positive and south as negative
1. Bullet one is fired in the north direction with the muzzle velocity $u$ . Find the velocity of the bullet as seen from the observer on the earth
a. $u+v$
b. $u-v$
c. $u$
d. $v$

2. find the velocity of the bullet as seen from the observer on the moving car
a. $u+v-w$
b. $u-v-w$
c. $u$
d. $v$

3.Second Bullet is fired in the south direction with the muzzle velocity $u$.Find the velocity of the bullet as seen from the observer on the earth
a. $u+v$
b. $v-u$
c. $u$
d. $v$

4.find the velocity of the second bullet as seen from the observer on the moving car
a. $u+v-w$
b. $v-u-w$
c. $u$
d. $v$


B. A train is moving in the west direction with a velocity 15m/s.A monkey runs on the roof of the train against its motion with a velocity 5m/s with respect to train .Take the motion along west as positive
5.Velocity of train relative to its driver
a. 0
b. 15 m/s
c. -15 m/s
d. 20 m/s

6. What is the velocity of train with respect to monkey
a. 5m/s
b -5 m/s
c. 15 m/s
d -15 m/s

7. find the velocity of monkey with respect to ground
a. 5 m/s
b. -5 m/s
c. 10 m/s
d. -10 m/s



link to this page by copying the following text

Note to our visitors :-

Thanks for visiting our website. From feedback of our visitors we came to know that sometimes you are not able to see the answers given under "Answers" tab below questions. This might happen sometimes as we use javascript there. So you can view answers where they are available by reloding the page and letting it reload properly by waiting few more seconds before clicking the button.
We really do hope that this resolve the issue. If you still hare facing problems then feel free to contact us using feedback button or contact us directly by sending is an email at [email protected]
We are aware that our users want answers to all the questions in the website. Since ours is more or less a one man army we are working towards providing answers to questions available at our website.


Class 11 Maths Class 11 Physics Class 11 Chemistry