Problem 3. In this problem, we aim to justify the term "conservative" for gradient fields. A gradient field F is called conservative because it conserves the total energy of a mass m as it moves within the field. Recall that the total energy is defined as: E =K+U=-m|v/+U. where K represents the kinetic energy, v the velocity of m, and U the potential energy associated with F. a) Use the relation: F=mr"(t), and show that W, the work done by a force field F to move a mass from point x1 to Xo is equal to: W = K(x1) - K(xo) b) Show that if F is conservative, that is, if F= -VU, where U is the potential energy, then the work W is equal to: W =U(Xo) - U(x1). and conclude that if F is conservative, then total energy E is constant