Q$2.$ It is desired to have the third joint of a $6-$axis robot go from an initial angle of $24$ deg to a final angle of $94$ deg in $5$ seconds. The robot starts with a velocity of $15$ deg $\frac{?}{sec}$ and should have a final velocity of $5$ deg$/$ sec$.$

a$.$ Calculate the coefficients for a third$-$order polynomial in joint$-$space trajectory.

b$.$ Determine the joint angles, velocities, and accelerations at $2$ and $4$ seconds.

c$.$ Determine the maximum velocity and accelorations during the trajectory.