A robot is to be driven from an initial position through two via points before it reaches its final destination using a $4-3-4$ trajectory. The positions, velocities, and time duration for the three segments for one of the joints are given below. Determine the trajectory equations and plot the position, velocity, and acceleration graphs for the joint.

${}_1=30,{}_1^{}=0,{}_1^{}=0,{}_{1i}=0,{}_{1f}=2$

${}_2=50,{}_{2i}=0,{}_{2f}=4,$

${}_3=90,{}_{3i}=0,{}_{3f}=2,$

${}_4=70,{}_4^{}=0,{}_4^{}=0,$