# Warp Speed and Relativity

The theory of relativity states that as an object travels with velocity v, its rest mass $m_0$ changes to a mass m given by the formula $m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$ where c is the speed of light.

By what factor is the rest mass of a spaceship multiplied if the ship travels at one-tenth the speed of light?

By what factor is the rest mass of a spaceship multiplied if the ship travels at one-half the speed of light?

By what factor is the rest mass of a spaceship multiplied if the ship travels at 90% the speed of light?

Warp speed is defined by the equation $v=w^3 c$. If an object’s mass is twice its rest mass, what warp is it travelling at?

Use the relativistic mass formula to show that it is not possible for an object with mass to travel faster than the speed of light.