Question

two cars are moving in opposite direction with velocity c/2 and c/3 find its relative velocity.

Answer 1

In classical physics, we would write

$u' = u+v$

when u and v are pointing into different directions.

Since u and v are relativistic speeds, we need to use relativistic velocity-addition formula instead:

$\displaystyle u' = \frac{u+v}{1+ \frac{uv}{c^2}} = \frac{c/2+c/3}{1+ \frac{1}{6}} = \frac{c/2+c/3}{1+ \frac{1}{6}} = \frac{5c}{6} \cdot \frac{6}{7} = \frac{5c}{7}$