L 8. A particle's velocity is described by the function '5' (t) = (et sin t, et, at cos t) for t E [0, 4]. (a) If the particle's initial position is ( %, 1, %), describe its position and acceleration as functions of t. Hint: %(et(sin t + cos t)) = Zet cost and %(et(sin t cos t)) = 2et sin t. (b) Verify that the particle's path lies on a circular cone of the form y2 = a2(:1(;2 + 22), and sketch the path. (c) What is the length of the particle's path from t = O to t = 4? (d) Parameterize the particle's position in terms of arc length. (e) Compute the curvature of the space curve traced by the particle