# Special theory of relativity – problems and solutions

Special theory of relativity – problems and solutions

1. An object whose length is 60 m moves at a speed of 0.6 c (c = the speed of light). According to a stationary observer, what is the length of the object?

__Known :__

The proper length (L_{o}) = 60 meters

Object’s speed (v) = 0.6 c

__Wanted :__ The length contraction (L)

*c = **the speed of light*

*L*_{o}* = **the proper length*

*L = **the length contraction*

The length contraction (L) :

2. An event observed by a stationary observer for 12 seconds. What is the time interval of the event, according to an observer who moving at a speed of 0.8 c (c = the speed of light).

__Known :__

The time interval of the event according to a stationary observer (t_{s}) = 12 seconds

The speed of observer (v) = 0.8 c

__Wanted:__ The time interval of the event according to an observer who moving at a speed of 0.8 c (t_{m})

__Solution :__

The equation of the time dilation :

*t*_{s}* = **the time interval according to a stationary observer*

*t*_{m}* = **the time interval according to a moving observer*

The time interval according to a moving observer (t_{m}) :