A particle’s velocity is described by the function ~v(t) = he t , et sin(t), et cos(t)i for t ∈ [0, 5].

(a) If the particle’s initial position is (2, 3, 1), describe its position and acceleration.
(b) What is the length of the particle’s path from t = 0 to t = 5?
(c) Parameterize the particle’s position in terms of arc length.
(d) Compute the curvature of the space curve traced by the particle.