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The velocity vectors of a point \( A \) varies with time as \( \vec{v}=a \hat{i}+b t \hat{j} \), where \( a \) and \( b \) are positive constants. Find the equation of trajectory of the point.
\( \mathrm{P} \)
(A) \( y=\frac{1}{2} b \frac{x^{2}}{a^{2}} \)
(B) \( y=\frac{1}{2} a \frac{x^{2}}{b} \)
(C) \( y=\frac{1}{2} a \frac{x}{b} \)
(D) \( y=\frac{1}{2} b \frac{x}{a} \)
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