Work, Energy and Power

Chapter 4 solved motion by tracking forces instant by instant. This chapter offers a shortcut so powerful it becomes the preferred tool for the rest of physics: follow the energy instead. It opens with the scalar product $\vec{A}\cdot\vec{B} = AB\cos\theta$, then defines work $W = \vec{F}\cdot\vec{d}$ — and immediately shows that work can be positive, negative or zero, so a force perpendicular to the motion does none at all. From there comes kinetic energy $K = \frac{1}{2}mv^2$ and the work-energy theorem $W_{net} = \Delta K$, proved for constant and then for variable forces, where work becomes the area under the force-displacement graph. Conservative forces earn a potential energy with $F = -\frac{dV}{dx}$, giving gravitational $V = mgh$ and spring $V = \frac{1}{2}kx^2$, and their sum with kinetic energy is conserved: $K + V =$ constant. Power $P = \frac{dW}{dt} = \vec{F}\cdot\vec{v}$ measures how fast the work is done, and the chapter closes with collisions, where momentum is always conserved but kinetic energy only sometimes is. Work, Energy and Power is high-weightage in both JEE Main and NEET, and its energy method quietly solves problems that would be brutal with forces alone.