$5-19($modified$)$ Suppose we desire a joint$-$space trajectory $q_i^d(t)$ for the $i^{th}$ joint $($revolute$)$ that

begins at rest at position $q_0$ at time $t_0$ and reaches position $q_1$ at time

$t_1=2sec$ with a final velocity of $q_1=1ra\frac{d}{sec}.$ Please,

analytically determine the cubic polynomial satisfying these constraints, and

use MATLAB to plot the joint$-$space trajectory of this joint for the interval $t_0$ to $t_1$

assuming $q_0=\frac{}{4}$rad and $q_1=-\frac{}{2}$rad.