A car approaches you at \(50 \mathrm{km} / \mathrm{h}\). The driver turns on the headlights. From your point of view, the light from the headlights is moving at a. \(c+50 \mathrm{km} / \mathrm{h}\) b. \(c-50 \mathrm{km} / \mathrm{h}\) c. \((c+50 \mathrm{km} / \mathrm{h}) / 2\) d. \(c\)

Special relativity is a theory formulated by Albert Einstein in 1905. It transformed our understanding of time, space, and motion by introducing the concept that the laws of physics are the same for all non-accelerating observers, and notably, that the speed of light in a vacuum is constant and independent of the motion of the light source or the observer. This theory arises from two postulates:
• The laws of physics are identical in all inertial frames of reference.
• The speed of light in vacuum is the same for all observers, no matter their relative motion or the motion of the light source.
Special relativity defies our everyday experiences and classical mechanics, especially at high speeds close to that of light. A major consequence is time dilation and length contraction, implying moving clocks run slower and lengths contract in the direction of motion.

The speed of light, denoted as \(c\), is an astonishing 300,000 km/s (or approximately 186,000 miles per second). Einstein’s theory of special relativity states that this speed is absolute and invariant. Whether you are moving towards a light source, away from it, or standing still, the speed at which light reaches you remains \(c\). This principle leads to various mind-bending consequences:
• Light takes the same time to travel equal distances, regardless of the observer’s movement.
• The addition of speeds works differently than in classical mechanics. For example, if a car moving at 50 km/h switches its headlights on, classical mechanics would expect you to see the light speed as \(c + 50\) km/h. However, relativity assures that it’s simply \(c\) from every viewpoint.

In classical mechanics, relative velocity is computed by simply adding or subtracting the velocities of objects depending on their direction of motion. However, in the context of special relativity, things behave differently due to the constancy of the speed of light. This uniqueness shows especially clear with high-speed scenarios:
• For objects moving at non-relativistic speeds (much slower than the speed of light), ordinary addition and subtraction of velocities work well.
• For objects moving close to the speed of light, the relativistic velocity addition formula must be used, which ensures the resultant velocity never exceeds \(c\).
In the exercise, regardless of a car approaching at 50 km/h, the light from its headlights moves at \(c\). This consistency illustrates one of the core tenets of special relativity: no matter the relative motion, light’s speed remains constant.