Final answer:
To find the curvature of a curve, find the magnitude of the second derivative of the position vector.
Step-by-step explanation:
Curvature of a curve is a measure of how much the curve bends at a given point. To find the curvature of the curve r(t) = 9ti + 9tj + (2t²)k, we need to find the magnitude of the second derivative of the position vector.
First, find the first derivative of r(t) to get the velocity vector v(t). Then, find the second derivative of r(t) to get the acceleration vector a(t). Finally, calculate the magnitude of a(t) to determine the curvature of the curve at any given point.
In this case, the position vector r(t) = 9ti + 9tj + (2t²)k has a constant curvature of 18 m/s².