# Time Dilation Formula

According to the theory of relativity, time dilation is defined as the difference between the 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 the other is moving along with the speed of light. The existence of time difference between the two clocks is known as time dilation.

## Formula of Time Dilation

The time dilation formula is given by,

$T\,&space;=\,&space;\frac{T_{0}}{\sqrt{1-\,&space;\frac{V^{2}}{C^{2}}}}$

Where,

• T is the time observed
• T0 is the time observed at rest
• v is the velocity of the object
• c is the velocity of light in a vacuum ($3\times 10^{8}m/s^{2}$)

## Solved Examples

Example 1

Determine the relativistic time, if T0 is 7 years and the velocity of the object is 0.55c.

Solution:

Given:

T0 = 7 years

v = 0.55c

The Formula for time dilation is given by,

$T\,&space;=\,&space;\frac{T_{0}}{\sqrt{1-\,&space;\frac{V^{2}}{C^{2}}}}$

$T=\frac{7}{\sqrt{1-\frac{(0.55^{2})(3^{2}\times 10^{16})}{3^{2}\times 10^{16}}}}$
$T=\frac{7}{\sqrt{1-0.55^{2}}}$
T=7/0.8351

T = 8.38 years

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