Problem 1

Consider a particle moving with position vector .

(a). Compute the Speed of the Particle

(b). Compute the Unit Tangent Vector

(c). Find the Principal Normal Vector

(d). Compute the Curvature

(e). Compute the Acceleration

(f). Compute , the Second Derivative of Distance with respect to time

(g). Using Your Answers to part (a)-(f), Verify the Formula

Problem 2

Let be the parameterized curve given by .

(a). Find the Length of from the point to

(b). Re-parameterize by Arc Length Starting at and Going in the Positive Direction

Problem 3

Evaluate the integral where is the line segment from to .

Problem 4

The position of an object with mass at time is where and are nonzero constants.

(a). Compute , the Force Acting on the Object at time

(b). Compute the Total Work Done by the Force on the Object during the Interval