A particle of mass ' m ' is moving in time ' t ' on a trajectory given by r =10 α t^2 i +5 β(t-5) j Where α and β are dimensional constants. The…

A particle of mass ' $\displaystyle m$ ' is moving in time ' $\displaystyle t$ ' on a trajectory given by $$\vec{r}=10 \alpha t^2 \hat{i}+5 \beta(t-5) \hat{j} $$ Where $\displaystyle \alpha$ and $\displaystyle \beta$ are dimensional constants. The angular momentum of the particle becomes the same as it was for $\displaystyle t=0$ at time $\displaystyle t=$ \_\_\_\_ seconds.