Given the curve C in parametric form:
C : x =2cos(t) , y=2sin(t), z =2t; 0≤tπ≤2π
Find each of the following in terms of t :
a) The velocity v(t)
b) The speed ds/dt
c)The acceleration a(t)
d) The unit tangent vector T(t)
e)The curvature k and the normal vector N(t)
f) The binormal vector B(t)
g) The tangential and normal components of acceleration
a) v = <x',y',z'>
b) speed = |v|
c) a = <x",y",z">
I'm sure your differential geometry text (or google) has formulas for T,N,B, etc.