Work is the process of transferring energy into or out of a system by applying a force over a distance.

Energy an object possesses due to its motion.

Energy stored in an object due to its position in a gravitational field.

Energy stored in a spring or other elastic material when it's stretched or compressed.

Energy associated with the random motion of atoms and molecules within a system, often appearing as heat or sound.

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

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 $a = \frac{v_f^2 - v_i^2}{2d}$ 4. Substitute: $W = mad = m(\frac{v_f^2 - v_i^2}{2d})d = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2 = ΔK$