Question $05-02$

A two$-$dimensional velocity field on a unitless $($dimensionless$)$ basis is given by the expression:

vec$(V)=[x^2-2y^2+2x]vec(i)+[3xy+y]vec(j).$

$($a$)$ Identify ALL stagnation points in the velocity field.

At $(x,y)=(2,2),$ determine dots

$($b$)$ the acceleration.

$($c$)$ the component of the velocity pointing in the direction of $=32$

$($d$)$ the direction that the particle is traveling.

$($e$)$ the direction that the particle is accelerating.

$($f$)$ if the particle is speeding up or slowing down. $($Hint: This is the same as the acceleration in the direction of velocity.$)$

$($g$)$ the vorticity.