<P> Notice that if the object were moving at the speed of light in the S system (i.e. u = c), then it would also be moving at the speed of light in the S ′ system . Also, if both u and v are small with respect to the speed of light, we will recover the intuitive Galilean transformation of velocities </P> <Dl> <Dd> u ′ ≈ u − v . (\ displaystyle u' \ approx u-v \ .) </Dd> </Dl> <Dd> u ′ ≈ u − v . (\ displaystyle u' \ approx u-v \ .) </Dd> <P> The usual example given is that of a train (frame S ′ above) traveling due east with a velocity v with respect to the tracks (frame S). A child inside the train throws a baseball due east with a velocity u ′ with respect to the train . In nonrelativistic physics, an observer at rest on the tracks will measure the velocity of the baseball (due east) as u = u ′ + v, while in special relativity this is no longer true; instead the velocity of the baseball (due east) is given by the second equation: u = (u ′ + v) / (1 + u ′ v / c). Again, there is nothing special about the x or east directions . This formalism applies to any direction by considering parallel and perpendicular components of motion to the direction of relative velocity v, see main article for details . </P>

Write down postulates of special theory of relativity and also explain time dilation