A particle moving in the x y plane experiences a velocity dependent force F = k (v_y i +v_x j ), where v_x and v_y are the x and y components of its…

A particle moving in the $\displaystyle x y$ plane experiences a velocity dependent force $\displaystyle \overrightarrow{\mathrm{F}}=\mathrm{k}\left(v_y \hat{i}+v_x \hat{j}\right)$, where $\displaystyle v_x$ and $\displaystyle v_y$ are the $\displaystyle x$ and $\displaystyle y$ components of its velocity $\displaystyle \vec{v}$. If $\displaystyle \vec{a}$ is the acceleration of the particle, then which of the following statements is true for the particle?