Question

Find the radialand angular component of acceleration for the motion r=1+cos(θ), θ=e^-t at θ=π/2

Answer 1

Recall that (using ' to mean d/dt)
radial v = r'
angular v = rθ'

radial a = r" - θ'^2
angular a = rθ" + 2r'θ'
So, plugging in your functions,
r' = e^-t sinθ
r" = e^-t (cosθ - sinθ)
a' = -e^-t
a" = e^-t

So plug and chug. google and your text can provide further details and examples.