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Prove It $\displaystyle v = \int{\frac{dv}{dt}\,dt}$
$\displaystyle = \int{\sin{(\pi t)} - \sqrt{3}\cos{(\pi t)}\,dt}$
$\displaystyle = -\frac{1}{\pi}\cos{(\pi t)} - \frac{\sqrt{3}}{\pi}\sin{(\pi t)} + C_1$.
$\displaystyle x = \int{v\,dt}$
$\displaystyle = \int{-\frac{1}{\pi}\cos{(\pi t)} - \frac{\sqrt{3}}{\pi}\sin{(\pi t)} + C_1\,dt}$
$\displaystyle = -\frac{1}{\pi ^2}\sin{(\pi t)} + \frac{\sqrt{3}}{\pi ^2}\cos{(\pi t)} + C_1 t + C_2$.
Now if you have initial or boundary conditions, use them to find $\displaystyle C_1$ and $\displaystyle C_2$.