# Calculating velocities using Reference frames

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...

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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.
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