Problem 3. A vector field F is termed "conservative" because it conserves the total energy of a mass m in motion within this field. The total energy is defined as: E=K+U= ,m|v|2+U. where K represents kinetic energy, and U is the potential energy associated with F. a) Consider a scenario in which a mass m is following a smooth curve y(t) within a domain with a conservative force field F. Demonstrate that the total energy along the path, denoted as E(y(t) ), remains constant if the following relation holds: F=my"(t). This is a manifestation of Newton's second law, f=ma, where a represents acceleration, a concept familiar from high school physics. b) Show that the work performed by a conservative vector field F to transport a mass from point po to p1 is equal to: W = K(p1) - K(po), where K(p) denotes the kinetic energy of the mass at point p