We integrate acceleration to get velocity and integrate velocity to get position.

Taking the initial values of their integrals (definite integrals) we see that velocity is $\large\frac{2}{2}$$ (\cos 2 t)$ with initial velocity as zero and the position is $(t- \large\frac{1}{2} $$\sin 2t)$ and thus the position keeps increasing with time while it has an oscillating component $-\large\frac{1}{2}$$ \sin 2t$ and thus 'b' is correct answer