2. A particle moving along a curve in the xy-plane is at position (x(t), y(t)) at time ≥ 0. The particle moves in such a way that x(t) = 3 cos (√1+t·t) and y'(t) = -5+4√2+ sint. At time t = 0, the particle is at the point (0, 3).
(Note: Your calculator should be in radian mode.)
(a) Find the acceleration vector of the particle at time = 5. Show the setup for your calculations.
(b) Find the total distance traveled by the particle over the time interval 0 ≤154. Show the setup for your calculations.
(c) For 0 ≤ 4, find the time when the particle's vertical distance above the line y = 0 is greatest. Justify your answer.
(d) For 0 <<4, determine the time t when the line tangent to the path of the particle is vertical. Show the setup for your calculations.