A particle moves along a straight line with speed $v$. The particle decelerates and then changes direction. Its new speed is $\frac{v}{2}$. The new velocity has a component of $\frac{v}{4}$ in the same direction as the particle's original path. Through what angle has the particle turned?
- A$27^\circ$
- B$30^\circ$
- C$45^\circ$
- D$60^\circ$