The position of a particle in space at time t is r(t) as shown below. Find the particle's velocity and acceleration vectors. Then find the particle's speed and direction of motion at t = 1. Write the particle's velocity at that time as the product of its speed and direction. r(t) = (3 In (t + 1))i+t'j + -k 3 The velocity vector is v(t) = t + y i+ 2t j + 5 k (Type exact answers, using radicals as needed.) 3 The acceleration vector is a(t) = - i + 2 j+ - K. (1 + 1) 2 (Type exact answers, using radicals as needed.) The velocity vector at t = 1 written as a product of the speed and direction is v(1) = (JI( D)i + (Di + (CD)*]. (Type an exact answer, using radicals as needed.)The equation r(t) = (2 1) 1+ (21- 187) is the position of a partide in space at time I. Find the angle between the velocity and acceleration vectors at time t = 0. The angle between the velocity and acceleration vectors at time t = 0 is radians. (Type an exact answer, using It as needed.)