A particle of mass is acted on by a force at time . At the particle is positioned at the origin and has velocity vector given by . (Note that these conditions are at not !). Find the position vector for all .

Problem 2

The position of a particle at time is given by

(a). Compute the Velocity and Speed of the Particle at time

(b). Compute the Distance Travelled by the Particle after time

(c). Re-parameterize with respect to Arc Length Starting at point

(d). Compute the Curvature . Simplify Your Answer so that no Cosines or Sines Appear

Problem 3

Let be the triangle having vertices , , and . Compute the integral .

Problem 4

Find a parameterization of the part of the curve given by the intersection of the plane and the hyperboloid having positive x coordinate. Orient the curve in the direction of increasing .