Unit tangent, normal, binormal etc.

Find the vectors

T, N and B as well as the curvature and the torsion of;

r(t) = (t^3)/3i + (t^2)/2j for t>0

I parametrized the curve and got

r(s) = ((3s+1)^2/3 - 1)^3/2)/2i + ((3s+1)^2/3 - 1)/2i

and I then proceeded to find T(s) for which I calculated;

T(s) = (3s+1)^5/3((3s+1)^2/3 - 1)^5/2)i + (3s+1)^5/3j

**Is this the right answer?** or Am i going the right way about it this at all...? because using this answer for the unit tangent vector its going to take me ages to calculate N, B, curvature & torsion..

Any help would be greatly appreciated