# Driving car with (almost) the speed of the light and switch the headlights on [duplicate]

I'm curious what will happen if we 'drive' a car with (almost) the speed of light, and all of sudden we switch the car headlights on? Will the car headlights ray have double speed (speed of 600.000km/h) or that ray will never be seen?

• possible duplicate of Double light speed – user10851 Jun 29 '14 at 10:36

## 1 Answer

The speed of light in vacuum is invariant in any inertial reference frame. In your reference frame (if you could of course ride along the car) the light beam leaves the car at speed $c$. From the point of view of your friend who is watching you sitting on the pavement he will see the light leave at a speed which is given by the relativistic addition formula:

$u^{'} = \frac{u+v}{1+uv/c^2}$

Pluggin in c as both speeds $v$ & $u$ here we get: $\frac{2c}{2} = c$

We found that in both reference frames (and in extend in any inertial reference frame) the speed of light is always a constant $c$