12.4.1 Given the position vector of the particle moving along the circle 24:2 + 3'2 = 1, find the particle's velocity and acceleration vectors at the stated times. so) = (sin c): + (cos 0]; t z E and g 12.4.3 Given the position of a particle in space at time t, find the particle's velocitv and acceleration vectors. Then find the particle's speed and direction of motion at the given value oft. Write the particle's velocityr at that time as the product of its speed and direction. t) 2 (2 cos US + (3 sin 0} + daft, t = ir/Z 12.45 Motion along a circle. Each of the following equations in parts [all-(e) describes the motion ofa particle having the same path, the unit circle x2 + 3,2 = 1. Although the path of each particle in parts {aJ-(el is the same, the behavior, or "dynamics,\" of each particle is different. For each part, answer the following questions. i) Does the particle have constant speed? If so, what is its constant speed? ii) is the particle's acceleration vector always orthogonal to its velocity vector? iii} Does the particle move clockwise or counterclockwise around the circle? iv) Does the particle begin at the point (1,0)? Hr) = (cos EJE + (sin 0;", r 2 0 t) = cos(2t)i + sin(2t)j, t :2 0 t) = cos(t )i+sin(t E)f, t 2 0 t) = (cos it)? (sin 0}, t 2 0 F(t) = cos(t2)E+ sin(c?')j, t2 0 \"DP-Ova