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

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.

The object's kinetic energy increases.

Mechanical energy is not conserved, and some energy will be converted to thermal energy.

Elastic potential energy is stored in the spring.

The object's gravitational potential energy increases.

Kinetic energy is converted into thermal energy, reducing the object's kinetic energy and increasing the internal energy (temperature) of the object and the surface it's sliding on.