Imagine you are on a spaceship. a second spaceship rockets past yours at 0.5 cc. you start a stopwatch and stop it 10 seconds later. for an astronaut in the other spaceship, the number of seconds that have ticked by during the 10 seconds on your stopwatch

Explanation:

Given is the case of time dilation where the velocity of other spaceship is comparable to the velocity of light, i.e. relativistic velocity.

Given that:

velocity of the fast moving spaceship,

where c is the velocity of light.

times according to the other spaceship, (relativistic time)

For time dilation we have the equation as:

magnitude and direction