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