Problem 1

For the curve given by ,

(a). Find the Derivative

(b). Find the Second Derivative

(c). Find the Curvature at

Problem 2

Find the curvature of the plane curve at the point

Problem 3

Calculate when

Problem 4

For a plane curve ,

Use this equation to compute the curvature at the given point.

Problem 5

Find the curvature of the curve

Problem 6

Find the curvature of at .

Problem 7

For the curve given by

(a). Find the Unit Tangent Vector

(b). Find the Principal Normal Vector

(c). Find the Curvature

Problem 8

Consider the helix . Compute at

(a). Find the Unit Tangent Vector

(b). Find the Principal Normal Vector

(c). Find the Unit Binormal Vector

Problem 9

Suppose the position of a particle in motion at time is given by the vector parametric equation .

(a). Find the Velocity of the Particle at time

(b). Find the Speed of the Particle at time

(c). Find the time(s) when the Particle is Stationary. if there is More than One Correct Answer, Enter Your Answers as a Comma Separated List

Problem 10

A car drives clockwise at a constant speed around the track shown below.

The the Longest Acceleration Vector for the Car Occurs at what point and Points in what Direction

• [x] A. in toward the centre of the track
• [ ] B. out away from the centre of the track
• [ ] C. toward the top of the track
• [ ] D. toward the bottom of the track