A particle of mass $$m$$ is moving in time $$t$$ on a trajectory given by,
$$\vec{r} = 10\alpha t^2 \hat{i} + 5\beta (t - 5)\hat{j}$$
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.