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A body of mass \( m_{1} \) moving with an unknown velocity of \( v_{1} \hat{i} \), undergoes a collinear collision with a body of mass \( m_{2} \) moving with a velocity \( v_{2} \hat{i} \). After collision, \( m_{1} \) and \( m_{2} \) move with velocities of \( v_{3} \hat{i} \) and \( v_{4} \hat{i} \) respectively. If \( m_{2}=0.5 m_{1} \) and \( v_{3}=0.5 v_{1} \) then \( v_{1} \) is [JEE (Main) 2019]
(a) \( v_{4}-\frac{v_{2}}{4} \)
(b) \( v_{4}-v_{2} \)
(c) \( v_{4}+v_{2} \)
(d) \( v_{4}-\frac{v_{2}}{2} \)
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