1. Given the position function r(t) = (3t2 + 1, 4t - 3, sin(at)), find the velocity, speed, and acceleration of the object. 2. Given the (constant) acceleration vector a(t) = (0, 2), initial velocity vector vo = (5, -2), and initial position vector To = (-1, 2), find the velocity and position functions for t 2 0. 3. Suppose a ball is thrown from the height of 2 meters with an initial velocity vo = 162 + 163 + 20k meters per second. (a) Determine the position function r(t) assuming that acceleration is only due to gravity, that is, a(t) = -9.8k. (b) When and where does the ball hit the ground? (c) What is the highest height the ball reaches during its flight? (Hint: Find the maximum of the z-component of the path or find the point where the velocity is horizontal.) (d) (Optional: ) How will the results change if a southerly (from the south) wind produces an acceleration 2j