91Ó°ÊÓ

Velocity is the rate of change in position of an item in motion as seen from a specific frame of reference and measured by a specific time standard.

The velocity of galaxy 1 relative to galaxy 2 will be equal to the sum of the velocity of galaxy 1 relative to 3 and the velocity of galaxy 3 relative to 2. Galaxy 1 is moving away from galaxy 3 at a certain speed.

The velocity of the galaxy 1 relative to 3 is V₁₃ =$-4500$m/s.

The velocity of the galaxy 3 relative to 2 is V₃₂=$-2200$m/s.

Hence V₂₃ = $2200$ m/s.

Similarly, for galaxy 4:

$\begin{array}{rcl}{R}_4& =& \frac{V}{d}\\ & =& \frac{2830{\displaystyle \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}}{190MIY}\\ & =& 14.9\frac{km}{s×MIY}\end{array}$

Similarly, for galaxy 1:

$\begin{array}{rcl}{R}_1& =& \frac{V}{d}\\ & =& \frac{-4500{\displaystyle \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}}{300MIY}\\ & =& -15\frac{km}{s×MIY}\end{array}$

Similarly, for galaxy 5:

$\begin{array}{rcl}{R}_5& =& \frac{V}{d}\\ & =& \frac{6700{\displaystyle \raisebox{1ex}{$km$}\!\left/ \!\raisebox{-1ex}{$s$}\right.}}{450MIY}\\ & =& 14.9\frac{km}{s×MIY}\end{array}$

Taking the average without considering the negative sign

$\begin{array}{rcl}Averagerateofexplanation& =& \frac{14.7+14.9+15+14.9}{4}\\ & =& 14.9\frac{km}{s×MIY}\end{array}$

The rate of the expansion of the galaxy is $14.9$km/s per million light-years.

The light travels in one year is$=3×{10}^8×60×60×24×365.25$.

$1\mathrm{light}\mathrm{year}=9.47×{10}^{15}\mathrm{m}$

Hence 1 million light year.

$$\begin{gathered} d=9.47×{10}^{15}×{10}^8 \\ d=9.47×{10}^{21}m \end{gathered}$$

Distance in kilometer

$$\begin{gathered} \mathrm{d}=\frac{9.47×{10}^{21}}{1000}\mathrm{km} \\ \mathrm{d}=9.47×{10}^{18}\mathrm{m} \end{gathered}$$

The time taken will be calculated using the equation

$\begin{array}{rcl}V& =& \frac{d}{t}\\ 14.9& =& \frac{9.47×{10}^{18}}{t}\\ t& =& 6.35×{10}^{17}s\end{array}$

Time in years can be calculated as;

$\begin{array}{rcl}t& =& \frac{6.35×{10}^{17}s}{60×60×24×365.25}\\ t& =& 2.01×{10}^{10}years\end{array}$

Hence the age of the universe is 20 billion years.