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Time Dilation Formula

According to theory of relativity, time dilation is defined as the difference between elapsed time of the two events measured by either moving relative to each other located differently from gravitational mass or masses.

Let’s consider a clock kept in two different observers. One observer is at rest and other is moving along with the speed of light. The existence of time difference between the two clocks is known as time dilation.

The time dilation formula is given by,

Where

T = time observed,

T0 = time observed at rest,

v = velocity of the object, and

c = velocity of light in vacuum.

Example 1

Determine the relativistic time, if T0 is 7years and v is 0.55c.

Solution:

Given:

T0 = 7 years

v = 0.55c

Formula for time dilation is given by,

T = T0 / 1− v2/c2

  = 7 / 1−(0.55c)2 / c2

T = 7 / 1 − 0.552

7 / 0.6975

T = 10.035  = 11 years

Question 2: Calculate the time dilation if T0 is 15 years and v = 0.6c.

Solution:

Given:

T0 = 15 years and v = 0.6c

Formula for time dilation is given by,

T = T0 / √1−v2/c2

  = 15 / √1−(0.6c)2/c2

  = 15 / √1−0.62

  = 23.43 = 24 years