Special Relativity

According to Einstein's theory of Special Relativity, the speed of light in vacuum is:

If a spaceship moves at 0.8c relative to Earth, what is the time dilation factor (γ) experienced by the spaceship's clock as observed from Earth? (Use γ = 1/√(1 - v²/c²))

A muon created in the upper atmosphere moves towards Earth at 0.98c. Its proper lifetime is 2.2 μs. What is its dilated lifetime as observed from Earth?

Which of the following quantities remains invariant (unchanged) under Lorentz transformation?

If a rod of length 10 m is moving at 0.6c relative to an observer, what is the length measured by the observer?

Two events occur simultaneously in one inertial frame but are observed to be non-simultaneous in another frame moving relative to the first. This phenomenon is called:

A particle with rest mass m₀ moves with velocity v. Its relativistic momentum is given by:

Derive the expression for relativistic kinetic energy (K.E.) starting from total energy E = γm₀c² and rest energy E₀ = m₀c².

A spaceship travels from Earth to a star 8 light-years away at 0.8c. Calculate the time taken for the journey as measured by an observer on Earth.

Two spaceships move towards each other, each at 0.6c relative to Earth. What is the relative velocity of one spaceship as observed from the other? (Use relativistic velocity addition formula)