The position of a particle is given by $\mathbf{r} = (at^2)\mathbf{i} + (bt^3)\mathbf{j} + (ct^{-2})\mathbf{k}$, where $a$, $b$, and $c$ are constants.
A) What is the velocity as a function of time?
B) What is the acceleration as a function of time?
C) Suppose $a = 4.22 \text{ m/s}^2$, $b = -2.76 \text{ m/s}^3$, and $c = -85 \text{ m/s}^2$. What is the particle's speed, in m/s, at $t = 1.72 \text{ s}$?
D) Referring to the values given in part (c), what is the magnitude of the particle's acceleration, in $\text{m/s}^2$, at $t = 1.72 \text{ s}$?
