Radius of Curvature Application problem

[undrcvrbro]

Homework Statement

A factory has a machine which bends wire at a rate of 4 unit(s) of curvature per second. How long does it take to bend a straight wire into a circle of radius 8?

My professor likes to give us things we've never seen before on our weekend quizzes. The above is one such problem.

All that I can get from that problem statement is that k(t) must equal 4? Can anyone kind try and explain what they are actually asking?

 

[LCKurtz]

Hint: What is the relationship between the calculus radius of curvature $\rho$ for a general curve, and the radius $r$ of a circle in the case when the curve is a circle?