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Q$1.$ It is desired to have the third joint of a $6-$axis robot go from an initial angle of $34$ deg to a final angle of $94$ deg in $4$ seconds. Calculate the coefticients for a third$-$order polynomial joint$-$space trajectory and determine the joint angles, velocities, and accelerations at $1,2,$ and $3$ seconds. The robot starts with a velocity of $10$ deg$/$ sec and should have a final velocity of $25$ deg$/$sec$.$