Homework H$\mathrm{.}1.$B

Given: Particle P moves in the $xy-$plane in such a way that the position vector of P as measured from the origin O is given as a function of time as: vec$(r{)}_P=(-\frac{1}{6}{t}^3+\frac{1}{2}{t}^2)hat(i)+\frac{1}{12}{t}^4$hat$(j),$ with the position vector components given in terms of meters and time $t$ given in seconds. For this problem, $=\frac{1}{s^3},=\frac{1}{s^2}$ and $=\frac{1}{s^4}.$

Find: For this problem:

$($a$)$ At $t=2s,$ determine the velocity vec$(v{)}_P$ and acceleration vec$(a{)}_P$ vectors in terms of the hat$(i)$ and hat$(j)$ Cartesian unit vectors, as well as the angles $$ and $$ as measured from the direction of the positive $x-$axis.

$($b$)$ Repeat Part $($a$)$ above for $t=5s.$

Make a short concise sentence for both the given and find statements