Velocity of the river with respect to ground is given by \( v_{0} \). Width of the river is \( d...

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Velocity of the river with respect to ground is given by \( v_{0} \). Width of the river is \( d \). A swimmer swims (with respect to water) perpendicular to the current with acceleration \( a= \) \( 2 t \) (where \( t \) is time) starting from rest from the origin \( O \) at \( t=0 \). The equation of trajectory of the path followed by the swimmer is
(a) \( y=\frac{x^{3}}{3 v_{0}^{3}} \)
(b) \( y=\frac{x^{2}}{2 v_{0}^{2}} \)
(c) \( y=\frac{x}{v_{0}} \)
(d) \( y=\sqrt{\frac{x}{v_{0}}} \)
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