Work-Energy
Somewhat separate from Newton's Laws and the kinematic equations, the work-energy method can be used to solve certain problems in a simpler way. Looking under Common problems, we revisit some examples using new methods that we worked through previously with a kinematic approach.
The full vector calculus definition of work is below.
This is not needed for most introductory physics classes. With most problems, forces are constant so the equation simplifies. The main exceptions to this are when the problem is about a non-constant force like springs, gravity for orbits, or friction on curved surfaces. With gravity over short distances, friction on flat unchanging surfaces, or any other constant force, the following assumption can be made.
There's this concept you've probably heard of called conservation of energy, where the total amount of work in a system is constant. Energy may change from one form to another or transfer between objects, but by measuring the total mechanical energy (TME) at the initial conditions and adding the energy transferred into or out of the system, the final TME is also known.
Just like with kinematics, rates of change with respect to time are useful. For energy or work, the rate of change is called power, with units of J/s (joules per second) or W (watts). Most physics textbooks use the symbol W for work and P for power, but many engineering subjects use a dot above the symbol for a rate of change. Time derivatives add dots, and time integrals take them away; a derivative with respect to position uses different notations.
The next page outlines different common ways work can be stored.
This example problem is a block on a slope solved with the work-energy method.