Laws of Motion

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