A comet fragment follows the planar trajectory r(t)=⟨etcost,etsint⟩ for t measured in years, where distances are expressed in astronomical units (AU).
(a) Compute v(t) and a(t) in simplest form.
(b) Prove that the velocity vector v(t) is never orthogonal to the position vector r(t) for t≥0.
(c) Express a(t) as a linear combination A(t)r(t)+B(t)v(t) and find the scalar functions A(t) and B(t).
(d) Using your result from part (c), determine the tangential and normal components of the acceleration at t=0 and interpret their physical meanings.