Given,
The velocity of the spaceship in as observed by an observer at the earth, v=0.75c
The time interval as observed by the observer on the earth, t₁=2.5 s
The time elapsed in the ship's frame of reference is given by,
[tex]t_2=\frac{t_1}{\sqrt[]{1-\frac{v^2}{c^2}}}[/tex]On substituting the known values,
[tex]\begin{gathered} t_2=\frac{2.5_{}}{\sqrt[]{1-\frac{(0.75c)^2}{c^2}}} \\ =\frac{2.5}{0.66} \\ =3.79\text{ s} \end{gathered}[/tex]Thus the time elapsed for an observer in the spaceship is 3.79 s