What transformation equations are required when speeds approach the speed of light?
Answer
Lorentz transformations
When relative speeds become very high, the simple addition/subtraction of Galilean transformations breaks down, necessitating the more complex Lorentz transformations inherent to Special Relativity.

#Videos
What are frames of reference in physics? - YouTube
Reference Frames - YouTube
Related Questions
What fundamental components constitute a reference frame at its most basic level?What critical realization about motion is often credited to Galileo in classical mechanics?What law defines an inertial reference frame?What characterizes a non-inertial reference frame?Why do physicists introduce fictitious forces when working within a non-inertial frame?What transformation equations are required when speeds approach the speed of light?How is a point uniquely located in a three-dimensional reference frame?From the perspective of a friend stationary on the ground watching a train pass, what path does a ball tossed straight up by a passenger trace?What is the primary role of the brain when executing a reach for a coffee cup, regarding reference frames?What mathematical process relates coordinates between two different reference frames?