Reasoning: Albert Einstein formulated the Theory of Relativity, which includes the Special Theory of Relativity $\mathbf{(1905)}$ and the General Theory of Relativity $\mathbf{(1915)}$. These theories revolutionized our understanding of space, time, gravity, and the speed of light.

Reasoning: A frame of reference is a coordinate system or a fixed point relative to which the position and motion of objects are observed and measured. Motion is always described with respect to a chosen frame of reference.

Reasoning: Using the time dilation formula: $\mathbf{t =}$ $\frac{\mathbf{t}_{\mathbf{o}}}{\sqrt{\mathbf{1\ - \ }\frac{\mathbf{v}^{\mathbf{2}}}{\mathbf{c}^{\mathbf{2}}}}}$
Given: Proper time: $\mathbf{t}_{\mathbf{o}}\mathbf{= 5.0}\mathbf{\ }\mathbf{s}$ ; Observed time: $\mathbf{t = 10.0}\mathbf{\ }\mathbf{s}$
$\mathbf{\Longrightarrow}$ $\mathbf{10 =}$ $\frac{\mathbf{5}}{\sqrt{\mathbf{1\ - \ }\frac{\mathbf{v}^{\mathbf{2}}}{\mathbf{c}^{\mathbf{2}}}}}$ $\mathbf{\Longrightarrow}$ $\sqrt{\mathbf{1 -}\frac{\mathbf{v}^{\mathbf{2}}}{\mathbf{c}^{\mathbf{2}}}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}$ ; Squaring both sides.
$\mathbf{\Longrightarrow}$ $\mathbf{1 -}$ $\frac{\mathbf{v}^{\mathbf{2}}}{\mathbf{c}^{\mathbf{2}}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{4}}$ $\mathbf{\Longrightarrow}$ $\frac{\mathbf{v}^{\mathbf{2}}}{\mathbf{c}^{\mathbf{2}}}\mathbf{=}\frac{\mathbf{3}}{\mathbf{4}}$ $\mathbf{\Longrightarrow}$ $\frac{\mathbf{v}}{\mathbf{c}}\mathbf{\ }\mathbf{=}\sqrt{\frac{\mathbf{3}}{\mathbf{4}}}\mathbf{= 0.866}$
Therefore, $\mathbf{v = 0.866}\mathbf{\ }\mathbf{c}$

Reasoning: According to Einstein’s Special Theory of Relativity, the speed of light in a vacuum is constant $\mathbf{(c = 3.0 \times}\mathbf{10}^{\mathbf{8}}\mathbf{\ m}\mathbf{s}^{\mathbf{- 1}}\mathbf{)}$ for all observers, regardless of the motion of the source or the observer.

Reasoning: An inertial frame of reference is a frame that has zero acceleration. Such a frame may either be at rest or move with constant velocity in a straight line. Therefore, all the given statements describe an inertial frame.