A five-axis robot needs to perform a two-stage movement. In the first stage, the first joint needs to go from initial angle of 10 to a final angle of 75 in 5 seconds. In the second stage, the first joint needs to go from 75 to 120 in 3 seconds. The robot is at rest while start the whole process. The angular speed needs to be 1/6 rad/s when pass 75. It will be fully stopped at 105. In this problem, the angular position is defined as 0 (t), and the angular velocity is defined as 0 (t). The units used in this problem are radian and rad/s. Problem la) Based on the description, what is the initial condition of the first stage? The units used in this question are radian and rad/s. (A) 0(0) = 0.175rad (0) = Orad/s 10rad 0(0) (B) (C) (D) (E) (0) = Orad/s 1.31rad (B) (C) (D) (E) 0(0) (0) = 0.261rad/s 0(0) = 0.175rad (0) = 0.3rad/s 10rad 0 (0) (0) = 0.3rad/s Problem 1b) What is the angular position and angular velocity when t= 5 s? (A) 0(5)= 1.31rad (5) = Orad/s 0(5)1.31rad (5) = 1.31rad/s 0(5) 1.31rad = 0 (5) = 0.524rad/s (5)= 75rad (5) = Orad/s 0(5)= 75rad (5)= 0.524rad/s Problem 1c) Find the corresponding third-order polynomials for stage 1 (0 Problem 1d) Find the corresponding third-order polynomials for stage 2 (5