A $3$dof planar robot arm is assigned five key points along a nominal straight$-$line path at defined points in time. Consider a path between key points as a cubic polynomial. For the data given below, solve for the coefficent a$1($the coefficient of $t)$ for a cubic polynomial describing the $x$ component displacement between points along a nominal straight$-$line path at defined points in time.

$kp1=\{20,200,-90\}$;$kp2=\{160,200,-90\}$;

$V1=\{40,60,0\}$;$V2=\{40,860,0\}$;$t1=1,t2=3$