Question

An object moves with position function r(t)= Find eqns for r't, r''t, T(t), N(t), and k(t)

Answer 1

r(t) = cos(t pi) i + sin(t pi) j + 3t k
now you just need to use the direct formulas that must be given in the text you are referring to

is the text thomas and finney?

Answer 2

If you need formulas for r'(t), you just have to differentiate each of the coordinate functions, so:
r'(t)=<dcos(tpi)/dt, dsin(tpi)/dt, d3t/dt> is the speed vector.

For r''(t), do the same with r'(t).

I am not familiar with the names of the functions T, N and k.
Could that be something like curve length or normal vector?

Answer 3

Let me be more specific. I know how to get r't and r''t. I just need help with the others.

Answer 4

T is the Unit tangent Vector
M is the Principal unit normal vector
k is curvature

Answer 5

I followed the formulas in my book, but it came out to be really convoluted to the point that I'm not sure the teacher would give a problem like that. So I think I got it wrong.