(Solved): (1 point) A peg on the end of a rotating caank slides freely in the vertical guide shown in the dia ...

(1 point) A peg on the end of a rotating caank slides freely in the vertical guide shown in the diagram. The gulde is rigidly connected to a piston which moves horizontally. The crank rotates at a constant angular speed of 1 in a circle of radius \( r \) It is easy to show that the position of the piston is given by \[ P(t)=L+r \cos (t), \] since \( x(t)=r \cos (t) \) Find the velocity and acceleration of the piston: \[ \frac{d}{d t} P(t)= \] \[ \frac{d^{2}}{d t^{2}} P(t)= \]