The speed of light in a vacuum is the same for all observers.

Measurements of space, time and distance for a moving observer are changed relative to those for a stationary observer, giving rise to time dilation and length contraction.

The following relationship is used to describe time dilation.

$$ t'= \dfrac{t}{\sqrt{1-(\dfrac{v}{c}})^2} $$

It could also be written as $t’=t \gamma$, where $\gamma$ is the Lorentz factor, $\dfrac{1}{\sqrt{1-(\dfrac{v}{c})^2}}$.

In this formula, the Lorentz factor is greater than one, so $t’$ represents the time passed that is ‘dilated’ or time from the reference frame of the stationary observer, which is greater than $t$, which is the time passed from the reference frame of a moving observer.

The following relationship is used to describe length contraction.

$$ l'= l\sqrt{1-(\dfrac{v}{c}})^2 $$

It could also be written as $l’=l \gamma$, where $\gamma$ is the Lorentz factor, $\sqrt{1-(\dfrac{v}{c})^2}$.

In this formula, the Lorentz factor is less than one, so $l’$ represents the length measured that is ‘contracted’ or from the reference frame of the stationary observer, which is less than $l$, which is the length from the reference frame of the stationary observer.

The two above relationships can be used to solve problems involving time dilation, length contraction and speed.