A particle of mass $m$ is moving in time $t$ on a trajectory given by,
$$\vec{r} = 10\alpha t^{2}\hat{\mathrm{i}} + 5\beta(t - 5)\hat{\mathrm{j}}$$
where $\alpha$ and $\beta$ are dimensional constants.\\
The angular momentum of the particle becomes the same as it was for $t = 0$ at time $t =$ \_\_\_\_ seconds.