The figure shows a particle moving along a path modeled by r(t) = cos t + t sin t, sin t - t cos t.

The figure shows a particle moving along a path modeled by

r(t) = ⟨cos πt + πt sin πt, sin πt - πt cos πt⟩.

The figure also shows the vectors v(t) and a(t) for t = 1 and t = 2.(a) Find a_T and a_N at t = 1 and t = 2.(b) Determine whether the speed of the particle is increasing or decreasing at each of the indicated values of t. Give reasons for your answers.

t=1 Figure for 46 y t=2