Consider a particle moving on an elliptical path described by r(t) = a cos ti + b

Consider a particle moving on an elliptical path described by r(t) = a cos ωti + b sin ωtj, where ω = dθ/dt is the constant angular velocity.

(a) Find the velocity vector. What is the speed of the particle?

(b) Find the acceleration vector and show that its direction is always toward the center of the ellipse.