Problem $1$: A particle $P$ moves counterclockwise along the circular path shown. The center of

circle lies on the $Y$ axis and the $x$ axis is tangent to the path at $O.$ At the instant shown, the

particle is traveling at a speed of $v=4\sqrt[\phantom{2}]{2}\frac{m}{s},$ the speed of the particle is increasing at the rate

of $v^{}=3\sqrt[\phantom{2}]{2}\frac{m}{s^2},=1($radius of circle$),$ and $=45.$ Draw the unit vectors for the Normal$-$

Tangent and $\{$:vec$(u{)}_n)$ and Polar and $\{$:vec$(u{)}_{})$ coordinates located at the particle in the diagrams

below. Show$/$label clearly the angles and directions of the unit vectors.

Normal$-$Tangent

Find the $($i$)$ Cartesian, $($ii$)$ Normal$-$Tangent, and $($iii$)$ Polar components of the velocity and

acceleration vectors $($fill in the table given below $-$ show your calculations, if any, on the back of

the sheet$).$