Agnes makes a round trip at a constant speed to a star that is 16 light-years distant from Earth, while twin brother Bert remains on Earth. When Agnes returns to Earth, she reports that she has celebrated 20 birthdays during her journey. (a) What was her speed during her journey

Speed of Agnes during her journey was 0.848c

Explanation:

Given that;

Age of Agnes t₀ = 20 years

distance d = 2 × distance of star from Earth = 2 × 16 light-years

= 32 light-years

so get her speed speed; we use the following expression

Yvt₀ = d

( v / √(1 - ()²) )² = ( 32 light-years / 20 yrs )²

v² / (1 - ( v²/c²)) = ( 32 × c  / 20 )²

v² / (1 - ( v²/c²)) = 2.56 × c²  

v² / c²-v²/c² = 2.56 × c²  

v²c²  / c² - v²  = 2.56 × c²  

v²  / c² - v²  = 2.56

v²  = 2.56 (c² - v²)

v²  = 2.56 (c² - v²)

v²  = 2.56c² - 2.56v²

v² + 2.56v² = 2.56c²

3.56v² = 2.56c²

v² = (2.56/3.56)c²

v = √((2.56/3.56)c²)

so v = 0.848c

Therefore, Speed of Agnes during her journey was 0.848c