Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose an object A is traveling at a velocity of 100 m/s, and another object B is traveling at 105 m/s. With both the objects traveling through the same direction, taking A as a reference frame, the velocity of B would be 5 m/s (Is this actually right?). But, when they're traveling in opposite directions, how would one measure the velocity of B (with A as reference frame)..? Does it actually take a negative sign? - Sorry, if I have a misunderstanding...

share|cite|improve this question
up vote 2 down vote accepted

You're quite correct, you'd write the opposite velocity with a negative sign. You just need to decide what sign convention to use. In your example you're only considering motion in one dimension, so you could take motion to the right to be positive in which case motion to the left would be negative. Or you could take motion to the left positive and motion to the right negative. It doesn't matter what convention you use as long as you're consistent.

Suppose we take motion to the right to be positive so in your first example both A and B are moving to the right. The velocity that A measures is $v_B - v_A$, so in your first example it's 105 - 100 or 5 m/s. If B is moving in the other direction the velocity $v_B$ is -105 m/s. It's negative because it's moving to the left. The velocity A measures is now -105 - 100 or -205 m/s. The minus sign tells us the motion is to the left so A sees B moving to the left at 205 m/s.

share|cite|improve this answer
Hello John: (Sorry for asking a belated question) It came to me after I've noticed David's answer. So, when do we calculate relativistic velocity. Here, we've just calculated the differences. – Waffle's Crazy Peanut Sep 22 '12 at 13:40
The number $\gamma$ appears in lots of SR formulae, and it's defined as $\gamma = (1 - v^2/c^2)^{-0.5}$. As long as $\gamma$ is close to one you can approximate the motion as non-relativistic. – John Rennie Sep 22 '12 at 14:12

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.