Problem $3(25$ pts$)$

Consider the follower displacement requirements of the figure:

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Design a polynomial equation to represent the rise between $150$ and $180.$

The rise is between $150$ and $180,$ what is the value for $?(4$ pts$)$

Consider the rise between $150$ and $180,$ ljst all the boundary conditions properly. $(6$ pts$)($Hint: use the linear rise segment to determine the velocity boundary condition at $150$ degrees.$)$

Represent the displacement, velocity, and acceleration in general polynomial form with unknown coefficients. $(6$ pts$)$

Use the boundary conditions to list all of the equations needed to solve for the unknown coefficients. $(3$ pts$)$

Solve for all unknown coefficients. $(6$ pts$)$