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The position process $x_t$ satisfies $$ x_t = x_0 + t v_0 + \int_0^t W_s ds \;. $$ Because $\int_0^t W_s ds \sim \mathcal{N}(0,\frac{1}{3} t^3)$, a simple change of variables shows that $$ x_t \sim \mathcal{N}( x_0 + t v_0, \frac{1}{3} t^3) \;. $$