A test car starts

PROBLEMS

$3.$ The pin P is constrained to move in the slotted guides, which move at right angles to one another. Guide A is moving on the fixed horizontal shaft according to $x(t)=400e^{-t}(mm).$ At the same instant, Guide B is moving on the fixed vertical shaft according to $y(t)=100sin(2t)(mm).$ When $t=1s,$ determine the components of the velocity and acceleration of pin $P,$

a$)$ in Cartesian coordinates,

b$)$ in Normal and tangential coordinates,

c$)$ in Polar coordinates

d$)$ Also calculate the radius of curvature of the path followed by $P$ and sketch the shape of the path at his instant.