At time ttt seconds a particle, PPP, has position vector r\mathbf{r}r metres, with respect to a fixed origin, such that
r=(t3−4t2)i+(12t−t2)j \mathbf{r} = (t^3 - 4t^2)\mathbf{i} + (12t - t^2)\mathbf{j} r=(t3−4t2)i+(12t−t2)jFind the exact speed of PPP when t=3t = 3t=3.
A student claims that the magnitude of acceleration of PPP will never be zero. Determine whether the student's claim is correct. Fully justify your answer.
