6.A single-link manipulator with a revolt joint stopping at @ = 15 degrees. It is desired to move the joint in a smooth manner to O = 75 degrees in 3 seconds. Find the coefficients of a five order polynomial x(t) = Pot Pit + Pzt= + Pats + Pat* + Pats that accomplishes this motion and brings the manipulator to rest at the goal. The following boundary conditions are given Position Velocity Acceleration t = 0 15 0 0 + t = T 75 0 0 + Please answer the following questions: 1) give all six coefficients; 2) plot position, speed and acceleration profiles