1. Start with Work: $W = Fd$ 2. Newton's Second Law: $F = ma$ 3. Kinematics: $v_f^2 = v_i^2 + 2ad$ which can be rearranged to a = rac{v_f^2 - v_i^2}{2d} 4. Substitute: W = mad = m(rac{v_f^2 - v_i^2}{2d})d = rac{1}{2}mv_f^2 - rac{1}{2}mv_i^2 = ΔK

Kinetic Energy: Energy of motion, depends on mass and velocity. | Gravitational Potential Energy: Energy of position, depends on mass, gravity, and height.

Conservative Forces: Work done is independent of the path taken (e.g., gravity, spring force). Mechanical energy is conserved. | Non-conservative Forces: Work done depends on the path taken (e.g., friction, air resistance). Mechanical energy is not conserved, and some energy is converted to thermal energy.

Kinetic Energy: Energy of motion, depends on mass and velocity. Gravitational Potential Energy: Energy of position, depends on mass, gravity, and height.

Conservative forces: Work done is independent of path (e.g., gravity, spring force). Non-conservative forces: Work done depends on path (e.g., friction, air resistance).