How is kinetic energy derived from work?

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

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How is kinetic energy derived from work?

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

What are the steps to derive kinetic energy from work?

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

What are the differences between kinetic and gravitational potential energy?

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

What is the difference between conservative and non-conservative forces?

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).