At time t t\,t seconds a particle P P\,P has position vector r=[(3t3−t+3)i+(2t2+2t−1)j]\mathbf{r} = \left[(3t^3 - t + 3)\mathbf{i} + (2t^2 + 2t - 1)\mathbf{j}\right]r=[(3t3−t+3)i+(2t2+2t−1)j] m.
Differentiate r\mathbf{r}r to obtain the velocity of PPP.
Find an expression for the acceleration of P P\,P in terms of ttt.