State Einstein's postulates of special relativity and apply time dilation and length contraction to objects moving at relativistic speeds.

What this dot point is asking

You need to state Einstein's two postulates and apply the time dilation and length contraction equations to objects moving at speeds close to $c$.

Einstein's two postulates

The second postulate is the surprising one. In everyday life speeds add: if you throw a ball forward from a moving train, the ground observer sees the train speed plus the ball speed. But light does not behave this way - every observer measures the same $c$. Holding $c$ constant for everyone means time and distance must give way instead.

The Lorentz factor

All relativistic effects scale with the Lorentz factor:

At everyday speeds $v \ll c$, $\gamma \approx 1$ and there are no noticeable effects. As $v$ approaches $c$, $\gamma$ grows without limit.

Time dilation

A clock moving relative to an observer is measured to tick more slowly than an identical clock at rest with that observer.

The proper time is always the shortest. "Moving clocks run slow" is the catchphrase.

Length contraction

An object moving relative to an observer is measured to be shorter along its direction of motion.

Experimental evidence

Time dilation is not just theory. Muons created high in the atmosphere have such short half-lives that, classically, almost none should reach the ground. Because they travel near $c$, time dilation (from our frame) or length contraction (from theirs) means far more survive the trip than Newtonian physics predicts - a routinely observed result.