Time dilation in a car

TIME DILATION IN A CAR

Consider a car moving of mass one ton, length 2.5m moving at a velocity of 100kmph [62mph] or  [27.77m/s]. According to the theory of Special Relativity, the car will undergo changes in length, mass and time. The length contracts while time and mass increase. The change in length and mass is highly negligible, but the change in time is considerable over a period of time.

Let the time measured outside the car by an observer be T_S = 10minutes [600second]

The clock inside the car will move faster than the observer’s clock. The time inside the car is given by,

      

   T’ = γ*T

Where,  T’ - Time inside car (s)

              T – Proper time (s)

              γ – Relativistic gamma factor

              γ = 1/√[1-(v/c)²]

              c – Speed of light 3 x 10⁸ m/s  

              v – Velocity of car [27.77 m/s]

Substituting all values in the above equation, we get the time inside the car to be

T’ = 600.000000000002 s

The difference between both times T’ – T = 2picosecond

Thus for every 10minutes the clock inside the car runs 2picosecond faster that the observer’s clock. For 5hours the car gains 0.1nanosecond over the observer’s clock.