1. Consider an object moving along a parametric curve whose position vector at time t is given by r(t) = 3t + (t 2) j + (1 t) k. - (a) Compute the velocity v(t) and the acceleration a(t) of the object. (b) Compute the object's speed v(t) and the exact arclengths of the part of the curve between t = 0 and t = 2. (c) Find the unit tangent (or "direction of motion") vector function T(t). (d) Show that the curvature of the curve is zero, and explain what this means about the shape of the curve. (e) Describe the movement of the object. Include in your description the starting point r(0) and the direction of acceleration.