A particle of mass \( m \) moves with a variable velocity \( v \), which changes with distance c...

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A particle of mass \( m \) moves with a variable velocity \( v \), which changes with distance covered \( x \) along a straight line as \( v=k \sqrt{x} \), where \( k \) is a positive constant. The work done by all the forces acting on the particle, during the first \( t \) seconds is
(1) \( \frac{m k^{4}}{t^{2}} \)
(2) \( \frac{m k^{4} t^{2}}{4} \)
(3) \( \frac{m k^{4} t^{2}}{8} \)
(4) \( \frac{m k^{4} t^{2}}{16} \)
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