Curvature forumula of a planar trajectory

[Rhawk187]

Homework Statement

http://steam.cs.ohio.edu/~cmourning/problem1.jpg

If the image doesn't load (and it might not, although I'm not sure why), it can be found at:

http://steam.cs.ohio.edu/~cmourning/problem1.jpg

Homework Equations

Part of the problem is I'm not entirely sure what all the relevant equations are. This is a planar trajectory so the torsion is 0, so I've just included the first two Frenet-Serret equations at:

http://steam.cs.ohio.edu/~cmourning/equations1.pdf

The Attempt at a Solution

It is rather complicated equationally, so I felt more comfortable typing it in something other than this, you can find the work at:

http://steam.cs.ohio.edu/~cmourning/physics1.pdf

If I should put this somewhere else on the forums let me know, this is my first time.

 

[Dick]

Just call the curve parameter s=x. Then the curve is (x,y(x)). The tangent vector is (1,y'(x)). That makes the normalized tangent T=(1,y'(x))/(1+y'(x)^2)^(1/2). Now kappa=|dT/dx|. You have that in your solution. You have to find the vector that is dT/dx and find it's magnitude. Start differentiating.