Work and energy

The notes outline fundamental physics ideas about *work* and *energy* in a concise, step‑by‑step manner. Energy is introduced as the capacity to do work; it is a scalar quantity whose SI unit is the Joule (J). The discussion then focuses on *kinetic energy (KE)*, which is the energy possessed by a body because of its motion and is always positive. The expression for kinetic energy is given by the well‑known formula $text{KE} = frac{1}{2} mv^2$, where $m$ is mass and $v$ is velocity. The derivation starts with the kinematic equation $v^2 - u^2 = 2as$, which relates velocity, acceleration $a$, and displacement $s$. Rearranging gives acceleration as $a = frac{v^2 - u^2}{2s}$. Using Newton’s second law, force is $F = ma$, so work done $W = F cdot s$ becomes $W = m cdot frac{v^2 - u^2}{2s} cdot s$. Simplifying this for the case of initial velocity $u = 0$, the work expression reduces to $W = frac{1}{2} mv^2$, proving that the work done on an object equals the kinetic energy gained by it.