I only need help with b) , c) , d) and e) if possible. I solved for x(t) and y(t
ID: 2881032 • Letter: I
Question
I only need help with b) , c) , d) and e) if possible. I solved for x(t) and y(t) and found all the coefficients.
b) To find curvature from 0 < t < 1, would I do k(0) + k(1) for the curvature formula? k = |x'y'' - y'x''| / [(x')2 + (y')2]3/2 ?
c) maximum curvature applies when t=0 for the derivative correct?
d) To find length, would integral (from 0 to 1) ||r'(t)||dt work?
e) wouldn't the parametric equations be of r(t) from point (0,0) and (1,1) for the circular arc? How would I express this in parametric form?
The equation for r(t) should be:
r(t) = (3t3 - 2t4)i + (t + 3t2 - 5t3 + 2t4)j
The co-efficients were:
a0 = 0
b0 = 0
a1 = 0
b1 = 1
a2 = 0
b2 = 3
a3 = 3
b3 = -5
a4 = -2
b4 = 2
Explanation / Answer
I can tell you about b,c,d
b) for finding curvature from (0,1). just integrate the k with t limit 0 to 1
c)you have formula for curvature. just diffrentiate it and find t where derivative equal to zero
d) yes