### Mass Kinetic Energy from Virtual Work

From Newton's second law, (introduced in Eq.(B.1)), we can use d'Alembert's idea of*virtual work*to derive the formula for the kinetic energy of a mass given its speed . Let denote a small (infinitesimal) displacement of the mass in the direction. Then we have, using the calculus of differentials,

*kinetic energy*of mass traveling at speed . The quantity is classically called the

*virtual work*associated with force , and a

*virtual displacement*[544].

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