Let,t → Instantaneous time\( \vec{v} \) → Velocity in x-direction\( \vec{x} \) → Instantaneous position\( \vec{x_0} \)→ Initial positionThe relationship between Eulerian and Lagrangian approaches for velocity in x direction is given by _______

• A. \( \vec{v}(t, \vec{x}(\vec{x_0}, t)) = \frac{\partial \vec{x} (\vec{x_0}, t)}{\partial t} \)
• B. \( \vec{v}(t, \vec{x}(\vec{x_0}, t)) = \frac{\partial \vec{x_0} (\vec{x}, t)}{\partial t} \)
• C. \( \vec{v}(t, \vec{x_0}(\vec{x}, t)) = \frac{\partial \vec{x} (\vec{x_0}, t)}{\partial t} \)
• D. \( \vec{v}(t, \vec{x_0}(\vec{x}, t)) = \frac{\partial \vec{x_0} (\vec{x}, t)}{\partial t} \)